physics (dpp - 1)...10 one end of string which passes through pulley and connected to 10 kg mass at...

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PHYSICS (DPP - 1)[JEE MAIN + ADV.] DIVISION

NLM

TM

1. Find velocity of ring B (vB) at the instant shown. The string is taut and inextensible :

30°

60°

v = 1m/sA

vB

A

B

(A) 21

m/s (B) 43

m/s (C) 41

m/s (D) 1 m/s

2. Consider an atwood machine in an elevator. Let vP, vA and vB denote velocities of elevator, block Aand block B respectively in ground frame. The elevator is moving along the vertical direction withvelocity vp. Which of the following situations is not possible. [Arrows along with velocity representdirection of motion]

AB

(A) vP ; vA ; vB (B) vP ; vA ; vB(C) vP = 0; vA ; vB (D) vP = 0; vA ; vB

3. In the figure shown the velocity of different blocks is shown. The velocity of C is

(A) 6 m/s (B) 4 m/s (C) 0 m/s (D) none of these

4. A boat sailing in a pond is being pulled with the help of a rope. At the moment, when the ropemakes an angle with the water surface and the rope is pulled with velocity v, the velocity withwhich the boat approaches the bank is

v

(A) v (B) cos

v(C) v cos (D) v(1 – cos )


5. The value of VB will be

A

B

V = 1m/sA

(A) 1 m/s (B) 2 m/s (C) 3 m/s (D) 4 m/s

6. In the figure shown, the blocks A and B are connected with an inextensible string. If the block Bis pulled with a velocity of 5 m/s then it is observed that block A moves with 10 m/s. Find theangle (in degree) shown in the diagram

A

B

10 m/s

5 m/s

(A) 60° (B) 30° (C) 45° (D) 37°

7. What is relation between VA and VB if pulleys and string are ideal

A

B

30°

(A) VA = VB (B) VA = VB tan 30° (C) VA = VB cot 30° (D) VA = VB cos 30°

8. The velocity of A at an instant is 4m/s rightwards. Then the velocity of block B is

A

B

(A) 4 m/s downwards (B) 2 m/s upwards (C) 2 m/s downwards (D) 1 m/s upwards

9. Choose the relationship which governs the velocities of the four cylinders.

(A) vA + vB – 4vC + vD = 0 (B) 4vA – 8vB – 4vC + vD = 0(C) 4vA – 4vB – 4vC + vB = 0 (D) vA + vB – vC + vD = 0

10. The ratio of acceleration of pulley to the acceleration of the block is (string is inextensible)

PmF

(A) 0.5 (B) 2 (C) 1 (D) None of these



NLM

TM

1. In the figure shown the acceleration of A is j15i15 then the acceleration of B is : (A remains incontact with B)

/////////////////////////////////////////////////////////////37°

A

B

y

x

F

(A) i15 (B) i15 (C) i10 (D) i5

2. In the figure shown, find out the value of [assume string to be tight]

(A) tan–1(3/4) (B) tan–1(4/3) (C) tan–1(3/8) (D) None

3. System is shown in the figure and man is pulling the rope from both sides with constant speed‘u’. Then the velocity of the block will be

(A) 4u3

(B) 2u3

(C) 4u

(D) 2u

4. In the arrangement shown, all surfaces are frictionless. The rod R is constrained to move vertically.The vertical acceleration of R is a1 and the horizontal acceleration of the wedge W is a2. The ratio

21 aa is equal to

(A) sin (B) cos (C) tan (D) cot

5. System is shown in the figure. Assume that cylinder remains in contact with the two wedges. Thevelocity of cylinder is

(A) 2u3419 m/s (B)

2u13

m/s (C) u3 m/s (D) u7 m/s


6. A block B moves with a velocity u relative to the wedge A. If the velocity of the wedge is v asshown in figure, what is the value of so that the block B moves vertically as seen from ground.

Bu

A v

(A) cos–1

vu

(B) cos–1

uv

(C) sin–1

vu

(D) sin–1

uv

7. Two students analysed two different problems of mechanics involving constraint motion. Symbolshave their usual meaning.Student-A Student-B

y

x

vy

vx

x

y

Rodvy

vx

The vertical rod can move only The ends of the rods are slipping on thevertically and the wedge can move ground & the wall respectively.only horizontally.

xy

= tan xy

= tan

y = x tan y = x tan vy = vx tan vy = vx tan

(A) Student A is correct, B is wrong. (B) Student A is wrong, B is correct.(C) Both are correct. (D) Both are wrong.

8. Consider the following statements about the blocks shown in the diagram that are being pushedby a constant force on a frictionless table

3 kg 2 kg

1 kg

F

A. All blocks move with the same accelerationB. The net force on each block is the same Which of these statements are/is correct(A) A only (B) B only (C) Both A and B (D) Neither A nor B

9. Three solids of masses m ,m1 2 and m3 are connected with weightless string in succession and are

placed on a frictionless table. If the mass m3 is dragged with a force T, the tension in the string

between m2 and m3 is

(A) m

Tm m m

2

1 2 3(B)

mT

m m m 3

1 2 3(C)

m mT

m m m

1 2

1 2 3(D)

m mT

m m m

2 3

1 2 3

10. Three blocks of masses m ,m1 2 and m3 are connected by massless strings as shown on a friction-

less table. They are pulled with a force T N3 40 . If m kg,m kg 1 210 6 and m kg3 4 , the ten-

sion T2 will be

m 1 T1

m2 m 3 T2 T3

(A) 20 N (B) 40 N (C) 10 N (D) 32 N



NLM

TM

1. A car is moving in a circular horizontal track of radius 10m with a constant speed of 10m/s. Aplumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The anglemade by the rod with the track is -(A) zero (B) 30° (C) 45° (D) 60°

2. A man of mass m stands on a frame of mass M. He pulls on a light rope, which passes over apulley. The other end of the rope is attached to the frame. For the system to be in equilibrium,what force must the man exert on the rope ?

Mm

(A) (M + m)g (B) (M + m)g (C) (M – m)g (D) (M + 2m)g

3. Two monkeys of masses 5 kg and 4 kg are moving along a vertical rope, the former climbing upwith an acceleration of 2 m/s2 while the later coming down with a uniform velocity of 2 m/s.Tension in the rope at the fixed support is –

(A) 80 N (B) 100 N (C) 98 N (D) 108 N

4. A block is kept on a smooth inclined plane of angle of inclination 30º that moves with a constantacceleration so that the block does not slide relative to the inclined plane. Let F

1 be the contact

force between the block and the plane. Now the inclined plane stops and let F2 be the contact

force between the two in this case. Then F1/F2 is :

(A) 1 (B) 34

(C) 2 (D) 23

5.

R=5m

B 3m1mA

Find out the normal reaction at point A and B if the mass of sphere is 10 kg.(A) 80N, 60 N (B) 40N, 30 N (C) 50N, 60N (D) 80N, 50 N


6. The system shown in figure is in equilibrium. Find the magnitude of tension in each string ; T1, T2,T3 and T4. (g = 10 m/s–2)

60°30°T3

T1A

10 kg

BT4

T2

(A) 100 200 200N, N, ,200N

3 3 3N(B)

100 200200N,100N, N, N3 3

(C) 200 100N,200N, N,100N

3 3(D) None of these

7. Find the contact force between the 3 kg and 2kg block as shown in figure.

2kg3kgF = 25N2F = 100N1

A B

(A) 25N (B) 70N (C) 55N (D) 40N

8. Find the contact force between the block and acceleration of the blocks as shown in figure.

3kg5kg F = 30N2F = 50N1

AB

2kg

C

(A) N1=36N, N2 = 46N, a = 1m/s2

(B) N1 = 46N, N2 = 32N, a = 2 m/s2

(C) N1 = 36 N, N2 = 46N, a = 2 m/s2

(D) None

9. A 5 kg block has a rope of mass 2 kg attached to its underside and a 3 kg block is suspended fromthe other end of the rope. The whole system is accelerated upward is 2 m/s2 by an external forceF0.What is F0?

F0

5 kg

2 kg

3 kg

(A) 60 N (B) 120 N (C) 40 N (D) 200 N

10 One end of string which passes through pulley and connected to 10 kg mass at other end ispulled by 100 N force. Find out the acceleration of 10 kg mass. (g = 9.8 m/s2)(A) 1 m/s2 (B) 0.2 m/s2 (C) 3 m/s2| (D) 2 m/s2



NLM

TM

1. A force F acting on a particle of mass 5 kg placed on a smooth horizontal surface. F = 40 Ntremains constant but its vector rotates in a vertical plane at an angular speed 2 rad/sec. If a t =

0, vector F is horizontal, find the velocity of block at t = 4 sec.

(A) 1 m/s (B) 2 m/s (C) 2 m/s (D) 22 m/s

2. In the figure, a man of true mass M is standing on a weighing machine placed in a cabin. Thecabin is joined by a string with a body of mass m. Assuming no friction, and negligible mass ofcabin and weighing machine, the measured mass of man is

m

(A) mMMm

(B) mMMm

(C) M (D) depends on g

3. A block tied between two springs is in equilibrium. If upper spring is cut then the acceleration

of the block just after cut is 6 m/s2 downwards. Now, if instead of upper spring, lower

spring is being cut then the acceleration of the block just after the cut will be:

(A) 16 m/s2 (B) 4 m/s2 (C) cannot be determined (D) none of these

4. In the arrangement shown, neglect the mass of the ropes and pulley. What must be the value ofm to keep the system in equilibrium ? There is no friction anywhere.

m

30°M

(A) 1 (B) 2M (C) 2M

(D) 4M

5. A flexible chain of weight W hangs between two fixed points A & B which are at he same horizontallevel. The inclination of the chain with the horizontal at both the points of support is . What isthe tension of the chain at the end points?

(A) 2W

. cosec (B) 2W

. sec (C) W cos (D) 3W

sin


6. Acceleration of (1) w.r.t. rope is 5g upwards. Find acceleration of (2) w.r.t. rope so that blockremains at rest.

5m

m

m (1)

(2)

(A) 4g upwards (B) 12g upwards (C) 8g upwards (D) 16g upwards

7. A man is standing in a lift which goes up and comes down with the same constant acceleration.If the ratio of the apparent weights in the two cases is 2 : 1, then the acceleration of the lift is(A) 3.33 ms–2 (B) 2.50 ms–2 (C) 2.00 ms–2 (D) 1.67 ms–2

8. Three solid hemispheres of radii R each are placed in contact with each other, with their flat faceson a rough horizontal surface. A sphere of mass M and radius R is placed symmetrically on top ofthem. The normal reaction between the top sphere and any hemisphere, assuming the system tobe static, is

(A) Mg/3 (B) 6Mg (C) 3Mg (C) None

9. An elastic spring of force constant k and natural length 3l0 is cut into two parts so that theirnatural lengths are 2l0 and l0 respectively. One end of these springs are attached to points P andQ, on a fixed vertical wall and other ends are tied with a block of mass m.(A) In equilibrium the distance of block from the vertical wall is 4l0/3(B) In equilibrium the distance of block from the vertical wall is 5l0/3(C) The force constant of shorter part of the spring is 2k/3(D) The force constant of larger part of the spring is k/3

10. A ball is held at rest in position A by two light cords as shown in figure. The horizontal cord is nowcut and the ball swings to the position B. What is the ratio of the tension in the cord in positionB to that in initial position A before cutting ?

=30°

A B

(A) 3 (B) 3/4 (C) 1/2 (D) 1



NLM

TM

1. A mountain climber is sliding down a vertical rope. Her total mass including the equipments is 65kg. By adjusting the friction on the rope, she controls the tension force on the rope as a functionof time is shown in the fig. The speed of the mountaineer at the end of 2 sec if she starts fromrest is [Take g = 9.8 ms–2]

(A) 2.25 ms–1 (B) 4.5 ms–1 (C) 5 ms–1 (D) 2.5 ms–1

2. In the system of pulleys shown what should be the value of m1 such that 100gm remains at restw.r.t. ground :

(A) 180gm (B) 160gm (C) 100gm (D) 200gm

3. The minimum value of mass m required to lift the load M shown in figure is

(A) 8M

(B) 4M

(C) 16M

(D) M

4. Three blocks of mass 1 kg, 4 kg and 2 kg are placed on a smooth horizontal plane as shown in thefigure. The contact force between 1 kg block and 4 kg block is

1kg 4kg 2kg 120N 50N

(A) 100 N (B) 120 N (C) 50 N (D) 110 N

5. For the system shown in figure, m1 > m2 > m3 > m4. Initially, the system is at rest in equilibriumcondition. if the string joining m4 and ground is cut, then just after the string is cut :(i) m1, m2, m3 remain stationary.(ii) The value of acceleation of all the 4 blocks can be determined.(iii) Only m4 remains stationary.(iv) Only m4 accelerates.(v) All the four blocks remain stationary.

m2

m1

m3

m4

Ground

Now, choose the correct option.(A) All the statements are correct (B) Only I, II and IV are correct(C) Only II and V are correct (D) Only II and IV are correct.


6. A solid sphere of mass 2kg is resting inside a cube as shown in the figure. V = (5t ?i + 2t ?j )m/s.Here t is the time in second. All surfaces are smooth. The sphere is at rest with respect to thecube. What is the total force exerted by the sphere on the cube. (Take g = 10m/s2 & y-axis alongvertical)

(A) 29 N (B) 29 N (C) 26 N (D) 89 N

7. A monkey pulls along the ground mid point of a 10 m long light inextensible string connectingtwo identical objects A & B each of mass 0.3 kg continuously along the perpendicular bisector ofline joining the masses . The masses are found to approach each other at a relative accelerationof 5 m/s2 when they are 6 m apart. The constant force applied by monkey is :(A) 4 N (B) 2 N (C) 3 N (D) none

8. In the arrangement shown in figure, pulleys A and B are massless and the thread is inextensible.Mass of pulley C is equal to m. If friction in all the pulleys is negligible, then:

(A) tension in thread is equal to 12

mg.

(B) acceleration of pulley C is equal to g/2 (downward).(C) acceleration of pulley A is equal to g (upward).(D) accceleration of pulley A is equal to 2g (upward).

9. Two blocks are connected by a spring. The combination is suspended, at rest, from a stringattatched to the ceiling, as shown in the figure. The string breaks suddenly. Immediately afterthe string breaks, what is the initial downward acceleration of the upper block of mass 2m?

(A) 0 (B) 3g/2 (C) g (D) 2g

10. In the figure shown, find out acceleration of each block.

10kg

2kg 4kg

(A) 2 2 21 2 3

70 170 30a m/ s ,a m/ s ,a m/ s23 23 23

(B) 2 2 21 2 3

170 70 30a m /s ,a m/ s ,a m/ s23 23 23

(C) 2 2 21 2 3

30 170 70a m/ s ,a m/ s ,a m/ s23 23 23

(D) None of these



NLM

TM

1. A bus moves over a straight level road with a constant acceleration a. A boy in the bus in the busdrops a ball outside. The acceleration of the ball with respect to the bus and the earth arerespectively -

(A) a and g (B) a + g and g – a (C) 22 ga and g (D) 22 ga and a

2. In the given diagram, with what force must the man pull the rope to hold the plank in position?Weight of the man is 60 kgf. Neglect the weights of plank, rope and pulley.

(A) 15 kgf (B) 30 kgf (C) 60 kgf (D) 120 kgf

3. A mass 1 kg is suspended by a thread. It is(i) lifted up with an acceleration 4.9 ms–2

(ii) lowered down with an acceleration 4.9 ms–2

The ratio of tensions in the thread is -(A) 3 : 1 (B) 1 : 3 (C) 1 : 2 (D) 2 : 1

4. A man of weight mg is moving upwards in a rocket with acceleration 4g. His apparent weightinside the rocket will be -(A) zero (B) 4 mg (C) 5 mg (D) 1 mg

5. A block of metal weighing 2 kg is resting on a frictionless plane. It is struck by a jet releasingwater at a rate of 1 kg/sec and at a speed of 5 m/sec. The initial acceleration of the block will be-(A) 2.5 m/s2 (B) 5.0 m/s2 (C) 10 m/s2 (D) 25 m/s2

6. A person says that he measured the acceleration of a particle to be non zero while no force wasacting on the particle -(A) he is a liar(B) his clock might have run slow(C) his metre scale might have been larger than the standard(D) he might have used non inertial frame

7. A small sphere is suspended by a string from the ceiling of a car. If the car begins to move witha constant acceleration a, tension generated in the string is:

(A) mg (B) 22 agm (C) 22 agm (D) 22 a2gm

8. A man is standing on a weighing machine placed in a lift. When Stationary, his weight is recordedas 40 kg. If the lift is moved upwards with an acceleration of 2 ms–2, then the weight recorded inthe machine will be -(g = 10 ms–2)(A) 32 kg (B) 40 kg (C) 42 kg (D) 48 kg


9. A 60 kg man stands on a spring scale in a lift. At some instant he finds that the scale reading haschanged from 60 kg to 50 kg for a while and then comes back to the original mark . What shouldhe conclude?(A) the lift was in constant motion upwards(B) the lift was in constant motion downwards(C) the lift while in motion upwards, suddenly stopped(D) the lift while in motion downwards, suddenly stopped

10. The elevator shown in figure is descending with an acceleration of 2 ms–2. The mass of the blockA = 0.5 kg. The force exerted by the block A on the block B is (take g = 10 m/s2)

B

A 2 ms– 2

(A) 2 N (B) 4 N (C) 6 N (D) 8 N



NLM

TM

1. A weight W hangs from a rope that is tied to two other ropes that are fastened to the ceiling asshown in figure making angles and with the horizontal. The values of T1, T2 and T3 are –

T1 T2

T3

W

(A) )sin(sinW,

)sin(sinW

, W cos (B) )tan(sinW,

)sin(sinW

, W sin

(C) )sin(cosW,

)sin(cosW

, W (D) )tan(cosW,

)tan(cosW

, 2W

2. Two masses 40 kg and 30 kg are connected by a weightless string passing over a frictionlesspulley as shown in the following figure. The tension in the string will be -

30º

T

30º

T

(A) 188 N (B) 368 N (C) 288 N (D) 168 N

3. The system shown in figure is released from rest. After blocks have moved distance h/3, collar ‘B’is removed and block A & C continue to move. Speed of C before it hits ground is -

h

m

A

m C B

h/3

(A) gH34

(B) 3gH2 (C)

3gH13

(D) gH22


4. A heavy spherical ball is constrained in a frame as in figure. The inclined surface is smooth. Themaximum acceleration with which the frame can move without causing the ball to leave theframe.

30°

(A) g/2 (B) 3g (C) 3/g (D) 2g

5. All surfaces shown in figure are smooth. For what ratio m1 : m2 : m3, system is in equilibrium. Allpulleys and strings are massless.

30º

m1

m2

m3

(A) 1 : 2 : 1 (B) 2 : 2 : 1 (C) 2 : 1 : 2 (D) 1 : 2 : 2

6. All pulley shown in figure are light and there is no friction between pulley and string. Accelerationof pulley ‘P’ in figure is given by -

B

A

P

(A) g upward (B) g downward (C) zero (D) None of these

7. The massless string connecting slider A and mass B passes over two small massless smoothpulley, one which is attached to ‘A’. The end of strings are attached to mass B and roof as shown.Mass B has constant velocity V0 directed downwards. At the instant when YA = b, the magnitudeof acceleration of A is -

b

YA

BA

b

(A) b

V20 (B)

b2V2

0 (C) b4

V20 (D) None


8. In the figure shown the acceleration of A is Aa

= 15 i + 15 j , then the acceleration of B is(A remains in contact with B) -

37º

y

xB

(A) 6 i (B) –15 i (C) –10 i (D) –5 i

9. Two trolleys 1 and 2 are moving with acceleration a1 and a2 respectively in the same direction. Ablock of mass ‘m’ on trolleys 1 is in equilibrium from the frame of observer stationary w.r.t.trolleys 2. The magnitude of friction on block due to trolley is -

2a1a12

(A) m(a1 – a2) (B) ma2 (C) ma1 (D) None of these

10. A pulley is attached to one arm of a balance and a string passed round it carries two masses m1and m2. The balance is counter poised and the pulley is clamped so that m1 and m2 do not move.How much counter weight is to be reduced or increased to restore balance if the clamp isreleased ?

m1

m2

(A) )mm()mm(g

21

221

to be reduced (B) )mm()mm(g

21

221

to be increased

(C) )mm()mm(g

21

21

to be reduced (D) )mm()mm(g

21

21

to be increased



NLM

TM

1. n-blocks of different masses are placed on the fric-tionless inclined plane in contact. They are releasedat the same time. The force of interaction between (n– 1)th and nth block is –

m1

m2

m3 m4

1 2

3 4

n

(A) (mn–1 – mn)g sin (B) zero(C) mng cos (D) none of the above

2. In the adjoining figure if acceleration of M with respect to ground is a, then -

mMa

(A) acceleration of m with respect to M is a

(B) acceleration of m with respect to ground is 2a sin (/2)

(C) acceleration of m with respect to ground is a

(D) acceleration of m with respect to ground is a tan

3. A person of 50 kg stands on a 25 kg platform. He pulls on the rope which is attached to theplatform via the frictionless pulleys as shown in the figure. The platform moves upwards at aconstant rate if the force with which the person pulls the rope is -

(A) 500 N (B) 250 N (C) 25 N (D) none of these

4. A block is kept on a smooth inclined plane of angle of projection that moves with a constantacceleration so that the block does not slide relative to the inclined plane. If the inclined planestops, the normal contact force offered by the plane on the block changes by a factor -(A) tan (B) tan2 (C) cos2 (D) cot

5. A block of mass m is resting on a wedge of angle as shown in the figure. With what minimumacceleration a should the wedge move so that the mass m falls freely ?

ma

(A) g (B) g cos (C) g cot (D) g tan

6. In the figure, the wedge is pushed with an acceleration of 10 3 m/s2. It is seen that the blockstarts climbing upon the smooth inclined face of wedge. What will be the time taken by the blockto reach the top ?

1m

m

a = 10 3 m/s2

30º

(A) 52

s (B) 51

s (C) 5 s (D) 25

s


7. In the arrangement shown in figure wedge of mass M moves towards left with an acceleration a.All surfaces are smooth. The acceleration of mass m relative to wedge is –

60º

M

m

(A) a/2 (B) mMa2

(C) m

a)mM(2 (D)

ma)mM(

8. In fig, a mass 5 kg slides without friction on an inclined plane making an angle 30º with thehorizontal. Then the acceleration of this mass when it is moving upwards, the other mass is10 kg. The pulleys are massless and frictionless. Take g = 10 m/sec2.-(Given : mA = 5 kg, mB = 10 kg)

30º

10 kg

10 g

B A 5 kg

(A) .33 m/sec2 (B) 3.3 m/sec2 (C) 33 m/sec2 (D) None of these

9. Assuming all the surfaces to be frictionless, acceleration of the block C shown in the figure is –

C

3m/s2

a

B A 4m/s2

(A) 5 m/s2 (B) 7 m/s2 (C) 3.5 m/s2 (D) 4 m/s2

10. The tractor A is used to hoist the bale B with the pulley arrangement shown. If A has a forwardvelocity vA, determine an expression for the upward velocity vB of the bale in terms of x.

hmt Tractor

h

B

y A

x

(A) h

xvA (B) 22A

xh

xv21

(C) 22

A

xh

hv21

(D)

xhvA



FRICTION

TM

1. A block of mass m lying on a rough horizontal plane is acted upon by a horizontal force P andanother force Q inclined an angle to the vertical. The block will remain in equilibrium if thecoefficient of friction between it and the surface is –

Q

P

(A)

cosQmgsinQP

(B) sinQmg

QcosP(C)

sinQmg

cosQP(D)

sinQmg

QsinP

2. What is the maximum value of the force F such that the block shown in the arrangement, doesnot move ?

60º m = kg3

F µ =32

1

(A) 20 N (B) 10 N (C) 12 N (D) 15 N

3. A block ‘B’ is just fitting between two plane inclined at an angle ‘’. The combination of plane isinclined at angle ‘’ with horizontal. If coefficient of friction between block and the plane ‘’ isinsufficient to stop slipping, then acceleration of block is -

B

(A) g{sin – cos } (B)

)2/sin(

cossing

(C) g {sin – 2 cos cos /2} (D) g {sin – cos . sin (/2)}

4. Three blocks are arranged as shown in which ABCD is a horizontal plane. Strings are masslessand both pulley stands vertical while the strings connecting blocks m1 and m2 are also verticaland are perpendicular to faces AB and BC which are mutually perpendicular to each other. If m1

and m2 are 3 kg and 4 kg respectively. Coefficient of friction between the block m3 = 10 kg andsurface is = 0.6 then, frictional force on m3 is -

D

A B

C

m1

m2

m3

(A) 30 N (B) 40 N (C) 50 N (D) 60 N


5. The block of mass m is placed on a rough horizontal floor and it is pulled by an ideal string by aconstant force F as shown. As the block moves towards right on the floor, then the frictional forceon block -

F

m

(A) remains constant (B) increases (C) decreases (D) can not be calculated

6. A block A is placed over a long rough plank B of same mass as shown in figure. The plank isplaced over a smooth horizontal surface. At time t = 0, block A is given a velocity v0 in horizontaldirection. Let v1 and v2 be the velocities of A and B at time t. Then choose the correct graphbetween v1 or v2 and t :

B

v0A

(A)

v1 or v2

t

v1

v2(B)

v1 or v2

t

v1

v2(C)

v1 or v2

t

v1

v2(D)

v1 or v2

t

v1

v2

7. A given object takes n times as much time to slide down a 45º rough incline as it takes to slidedown a perfectly smooth 45º incline. The coefficient of kinetic friction between the object and theincline is given by -

(A)

2n

11 (B) 2n11

(C)

2n

11 (D)

2n11

8. Block A of mass M in the system shown in the figure slides down the incline at a constant speed.

The coefficient of friction between block A and the surface is 1

3 3 . The mass of block B is-

A

B 30º

(A) M/2 (B) M/3 (C) 2M/3 (D) M/ 3

9. A block of mass m is placed on a rough inclined plane of inclination kept on the floor of the lift.The coefficient of friction between the block and the inclined plane is . With what accelerationwill the block slide down the inclined plane when the lift falls freely ?(A) Zero (B) g sin – g cos (C) g sin + g cos (D) None of these

10. In the given figure the wedge is fixed, pulley is frictionless and string is light. Surface AB isfrictionless whereas AC is rough. If the block of mass 3m slides down with constant velocity, thenthe coefficient of friction between surface AC and the block is -

45º

A

3Mm

B C 45º

(A) 31

(B) 32

(C) 21

(D) 34



FRICTION

TM

1. Two blocks of masses 10 kg and 2 kg are connected by an ideal spring of spring constant 1000 N/m and the system is placed on a horizontal surface as shown.

10kg

µ=0.5

2kg

µ=0

The coefficient of friction between 10 kg block and surface is 0.5 but friction is assumed to beabsent between 2 kg and surface. Initially blocks are at rest and spring is unstreached then 2 kgblock is displaced by 1 cm to elongate the spring then released. Then the graph representingmagnitude of frictional force on 10 kg and time t. (time t is measured from that instant when 2kgis released to move)

(A)

t

f

(B)

t

f

(C)

t

f

(D) None of these

2. Two blocks each of mass 20 kg are connected by an ideal string and this system is kept on roughhorizontal surface as shown. Initially the string is just tight then a horizontal force F = 120 N isapplied on one block as shown.

F=120N 20kgd 20kgd

µ = 0.5 µ = 0.5If friction coefficient at every contact is µ = 0.5 then which of the following represents the correctfree body diagram.

(A)

N=200N

20kgd 20kgd

N= 200N

T=50NF= 120N

200NF2 = 70N

200NF1 = 50 N

T=50N

(B)

N=200N

20kgd 20kgd

N= 200N

T=20NF= 120N

200NF2 = 100N

200NF1 = 20 N

T=20N

(C)

N=200N

20kgd 20kgd

N= 200N

T=60NF= 120N

200NF2 = 60N

200NF1 = 60 N

T=60N

(D) All of the above

3. A block of mass m1 = 20 kg is kept on horizontal surface where coefficient of friction betweenblock and surface is µ = 0.75. This block is connected by an ideal string with another block ofmass m2. The string is passing over an ideal fixed pulley and the string between pulley and m2 isvertical as shown in the figure. Then the minimum value of mass m2 which can make m1 justmove on horizontal surface is (position of m1 on surface is not fixed you can adjust it to getminimum value of m2 and assume g = 10 m/s2).


µ/////////////////////////////////////// \\\\\\\\\

m1

m2

\\\\\\\\\\\\

(A) 12 kg (B) 14 kg (C) 16 kg (D) 20 kg

4. A particle moves on a rough horizontal ground with some initial velocity say v0. If 3/4th of itskinetic energy is lost in friction in time t0. Then coefficient of friction between the particle and theground is -

(A) 0

0gt2v

(B) 0

0gt4v

(C) 0

0gt4v3

(D) 0

0gtv

5. In the given figure, the coefficient of friction between m1 and m2 is µ and m2 and horizontalsurface is zero –

µ1 =

µ2 = 0

Fm1

m2

(A) If F > µm1g, then relative acceleration is found between m1 and m2

(B) If F < µm1g, then no relative acceleration is found between m1 and m2

(C) It F > µm1g, then both bodies move together(D) (A) and (B) are correct

6. A car starts from rest to cover a distance s. The coefficient of friction between the road and thetyres is . The minimum time in which the car can cover the distance is proportional to –

(A) (B) (C) 1

(D)

1

7. A flat car is given an acceleration a0 = 2m/s2 starting from rest. A cable is connected to a crateA of weight 50kg as shown. Neglect friction between the floor and the car wheels and also themass of the pulley. Calculate corresponding tension in the cable if = 0.30 between the crateand the floor of the car –

a0

50 kg

(A) 350 (B) 250 (C) 300 (D) 400

8. A spherical ball of mass 1/2 kg is held at the top of an inclined rough plane making angle 30ºwith the horizontal the coefficient of limiting friction is 0.5. If the ball just slides down the planewithout rolling its acceleration down the plane is –

(A)

4

32g (B) g (C)

4

132g (D)

2

13g


9. Two blocks A and B attached to each other by a massless spring, are kept on a rough horizontalsurface (µ = 0.1) and pulled by a force F = 200 N as shown in figure. If at some instant the 10 kgmass has acceleration of 12 m/s2, what is the acceleration of 20 kg mass ?

10kg 20kg F = 200 N

A B

µ=0.1(A) 2.5 m/s2 (B) 4.0 m/s2 (C) 3.6 m/s2 (D) 1.2 m/s2

10. A stationary body of mass m is slowly lowered onto a massive platform of mass M (M>>m)moving at a speed V0 = 4 m/s as shown in fig. How far will the body slide along the platform ? (µ= 0.2 and g = 10 m/s2)

M

m

V0 = 4m/s

(A) 4 m (B) 6 m (C) 12 m (D) 8 m



FRICTION

TM

1. Three blocks A, B and C of equal mass m are placed one over the other on a smooth horizontalground as shown in figure. Coefficient of friction between any two blocks of A, B and C is ½. Themaximum value of mass of block D so that the blocks A, B and C move without slipping over eachother is –

A.

C.

B.

D.

(A) 6 m (B) 5 m (C) 3 m (D) 4 m

2. In the figure, mA = 2 kg and mB = 4 kg. For what minimum value of F, A starts slipping over B :(g = 10 m/s2) –

µ1 = 0.2

BA

F

µ2 = 0.4(A) 24 N (B) 36 N (C) 12 N (D) 20 N

3. In the given figure (Take g = 10m/s2) –

A

B

C

D 7kg

3kg

2kg

1kg f = 10 N

g = 10 m/s2

µ1 = 0 .1

µ2 = 0.2

µ3 = 0.3

µ4 = 0.4

(A) the acceleration of A and B are same to each other(B) the acceleration of A is 9 m/s2

(C) the acceleration of B, C and D are not same to each other(D) all bodies move with common acceleration

4. A 40 kg slab rests on a frictionless floor. A 10 kg block rests on top of the slab. The staticcoefficient of friction between the block and slab is 0.60 while the kinetic coefficient is 0.40. The10 kg block is acted upon by a horizontal force 100 N. If g = 9.8 m/s2, the resulting accelerationof the slab will be -

40 kg 10 kg

100 N No friction

(A) 0.98 m/s2 (B) 1.47 m/s2 (C) 1.52 m/s2 (D) 6.1 m/s2

5. A body of mass 2 kg is placed on a horizontal surface having coefficient of kinetic friction 0.4 andcoefficient of static friction 0.5. If a horizontal force of 25 N is applied on the body, the frictional

force acting on the body will be: (g = 10 ms2 )

(A) 8 N (B) 10 N (C) 20 N (D) 25 N


6. The brakes of a car moving at 20 m/s along a horizontal road are suddenly applied and it comesto rest after travelling some distance if the coefficient of friction between t0he tyres and the roadis 0.90 and it is assumed that all four tyres behave identically, the shortest distance the carwould travel before coming to a stop is -(A) 2.27 m (B) 11.35 m (C) 22.7 m (D) 4.54 m

7. With reference to the fig. shown, if the coefficient of friction at all the surfaces is 0.42, then theforce required to pull out the 6.0 kg block with an acceleration of 1.50 m/s2 will be –

6 kg

2 kg

F

(A) 36 N (B) 24 N (C) 84 N (D) 51 N

8. Two blocks connected by a massless string slide down an inclined plane having angle of inclina-tion 37º. The masses of the two blocks are M1 = 4 kg and M2 = 2 kg respectively and thecoefficients of friction 0.75 and 0.25 respectively-

M1 = 4 kg

M2 = 2 kg

37º

(a) The common acceleration of the two masses is 1.3 ms–2

(b) The tension in the string is 14.7 N(c) The common acceleration of the two masses is 2.94 ms–2

(d) The tension in the string is 5.29 N(A) a, d (B) c, d (C) b, d (D) b, c

9. The coefficient of static friction between the two blocks is 0.363. What is the minimum accelera-tion of block 1 so that block 2 does not fall ?

1 2 a

(A) 6 ms–2 (B) 12 ms–2 (C) 18 ms–2 (D) 27 ms–2

10. Mass of upper block and lower block kept over the table is 2 kg and 1 kg respectively andcoefficient of friction between the blocks is 0.1. Table surface is smooth. The maximum mass Mfor which all the three blocks move with same acceleration is (g = 10 m/s2) –

2 kg 1 kg

µ = 0.1 µ = 0

m

(A) 1 kg (B) 2/3 kg (C) 1/3 kg (D) 3/4 kg

physics (dpp - 1)...10 one end of string which passes through pulley and connected to 10 kg mass at...

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