rotational motion

7/18/2019 Rotational Motion

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#Physics@ GURUKUL

#Rotational Motion Level – 1 Question for Practice

DPS-R11. A ball slides without friction down an inclined plane of

height2

R 5

.

It crosses the bottom of the inclined plane and moves

along a circular loop of radius R. The force exerted by the

ball at point A is

(a) mg (b) 2.5 mg

(c) 3.5 mg (d) 4.5 mg

2. A ball weighing 15 g is tied to a string 10 cm long. Initially

the ball is held in position such that the string is horizontal.

The ball is now released. A nail N is situated vertically below

the support at a distance L. The minimum value of L suchthat the string will be wound round the nail is

(a) 2 cm (b) 4 cm

(c) 6 cm (d) 8 cm

3. A block of mass M is placed on a horizontal frictionless

surface AB and a body P of mass m is released on its

frictionless slope.

As P slides by a length L on this slope of inclination θ,

the block Q would slide by a distance :

(a)M

mL cos θ (b)

mM

m

+L

(c)θ

+

cosmL

mM (d)

Mm

cosmL

+

θ

4. A body of mass M and radius R is rolling horizontally

without slipping with speed v. It then rolls up a hill to a

maximum height h. If h = 5v2/6g, what is the M.I. of the body

?

a)2

1MR 2 (b)

3

2MR 2

(c) 4

3

MR 2

(d) 5

2

MR 2

5. A boy and a man carry a uniform rod of length l horizontally

in such a way that the boy gets4

1th of the load. If the boy is

at one end of the rod, then the distance of the man from the

other end is

(a)3

l (b)

4

l (c)

3

l2 (d)

4

l3

6. A carpenter has constructed a toy as shown in the adjoining

fig.

If the density of the material of the sphere is 12 times

that of cone, the position of the centre of mass of the toy is

given by :

(a) at a distance of 2R from O

(b) at a distance of 3R from O

(c) at a distance of 4R from O

(d) at a distance of 5R from O

7. A certain bicycle can go up a gentle incline with constant

speed when the frictional force of ground pushing the rear

wheel if F2 = 4 N. With what force F1 must the chain pull onthe sprocket wheel if R 1 = 5 cm and R 2 = 30 cm ?

(a) 4 N (b) 24 N

c) 140 N d)4

35 N

8. A heavy disc is thrown on a horizontal surface in such a way

that it slides with a speed V0 initially without rolling. It wil

start rolling without slipping when its speed reduces to :

(a)2

V0 (b)3

V2 0

(c)5

V3 0 d)7

V5 0

9. A heavy particle hanging from a string of length l is projected

horizontally with speed gl . The speed of the particle at the

point where the tension in the string equals the weight of the

particle is

(a) )gl2( (b) )gl3(

(c) )2/gl( (d) )3/gl(

10. A mass m is supported by a massless string wound around a

uniform cylinder of mass m and radius R, Fig. With what acc

will the mass fall on release ?

(a) 2g/3 b) g/2

c) g (d) 4g/3

11. A particle of mass m = 5 is moving with a uniform speed v =3√2 in the XOY plane along the line y = x + 4. The

magnitude of the angular momentum about origin is

(a) zero b) 60 unit

(c) 7.5 unit (d) 40 √2

12. A particle of mass m is rotating in a plane in circular path of

radius r. Its angular momentum is L. The centripetal force

acting on the particle is

O

4R

2R

M

A

C

BQ

P

5R/2

600

600



(a)mr

L2

b)2

2

r

m L

c)3

2

mr

L d)

2

mr

L.

13. A particle originally at rest at the highest point of a smooth

vertical circle is slightly displaced. It will leave the circle at a

vertical distance h below the highest point, such that(a) h = R b) h = 2R

(c) h = R/2 (d) h = R/3

14. A rigid body rotates about a fixed axis with variable angular

velocity equal to α - βt at time t where α and β are constants.

The angle through which it rotates before it comes to rest is :

(a)β

α2

2

(b)α

β−α

2

22

(c)ββ−α

2

22

(d)2

)( β−αα

15. A ring rolls down, starting from rest, down an inclined plane

of length l and inclination θ. The velocity of the centre of

mass of the ring at the mid-point of the inclined plane is

(a) θ singl (b)2

singl θ

(c) θ singl2 (d) θ singl7

4

16. A thick walled hollow sphere has outer radius R. It rolls

down an inclined plane without slipping and its speed at the

bottom is v. If the inclined plane is frictionless and the sphere

slides down without rolling, its speed at the bottom will be

5v/4. What is the radius of gyration of the sphere?

(a)2

R (b)

2

R

(c)4

R 3 (d)

4

R 3

17. A uniform circular disc of radius a is taken. A circular portion

of radius b has been removed from it as shown in the fig.

f the centre of hole is at a distance c from the centre ofthe disc, the distance x2 of the centre of the mass the

remaining part from the initial centre of mass O is given by :

a)) ba(

b22

2

−

π (b)

) ba(

cb22

2

−

−

(c)) ba(

c22

2

−

π (d)

) bc(

a22

2

−

π

18. A uniform cylinder has a radius R and length L. If the

moment of inertia of this cylinder about an axis passing

through its centre and normal to its circular face is equal to

the normal of inertia of the same cylinder about an axis

passing through its centre and normal to its length l then :

(a) L = R (b) L = 3 R

(c) L =3

R (d) L = 0

19. A uniform solid right circular cone of base radius r is joined

to a uniform solid hemisphere of radius r and of the same

density, so as to have a common face. The centre of gravityof the composite solid lies on the common face. The height of

the cone is

a) 3r/ 2 (b) r/ 6

c) 4r (d) r 3

20. Angular momentum and areal velocity of a body of mass m

are related as

a) L = 2m × areal velocity

b) L = 2π × areal velocity

c) Areal velocity = 2mL

(d) 2m = 2 × areal velocity

21. Consider the rotation of a rod of mass m and length l from

position AB to AB/.

Which of the following is correct ?

a) Weight of the rod is lowered by2

l.

b) Loss of gravitational potential energy is2

1mgl.

(c) Angular velocity is l

g3 .

(d) Rotational kinetic energy is3

ml 22ω

22. Fig. shows a thin metallic triangular sheet ABC.

The mass of the sheet is M. The moment of inertia of the

sheet about side AC is :

(a)18

Ml2

(b)12

Ml2

(c)6

Ml2

(d)4

Ml2

23. From a given sample of uniform wire, two circular loops P

and Q are made, P of radius r and Q of radius nr. If the M.I

of Q about its axis is 4 times that of P about its axis

(assuming wire diameter much smaller, than either radius)

the value of n is :

A B

C

l

l

A B

B’

ab

cO



(a) (4)2/3 b) (4)1/3

c) (4)1/2 d) (4)1/4

24. If a disc slides from top to bottom of an inclined plane, it

takes time t1. If it rolls, it takes time t2. Now,21

22

t

t is

(a)2

1 (b)

3

2

(c)23 (d)

52

25. If a sphere is rolling, the ratio of the translational energy to

total kinetic energy is given by

a) 7:10 b) 2:5

(c) 10:7 d) 5:7

26. If the earth is treated as a sphere of radius R and mass M, its

angular momentum about the axis of its diurnal rotation with

period T is

(a)T5

MR 4 2π

(b)T

MR 2 2π

(c)π 2

TMR 2 (d)

T

MR 3π

27. In fig. (a), a metre stick, half of which is wood and the other

half steel is pivoted at the wooden end at O and a force F is

applied to the steel end A.

In fig. (b) the stick is pivoted at the steel end at O’ and

the same force F is applied at the wooden end at A’. The

angular acceleration:

(a) in (a) is greater than in (b)

(b) in (b) is greater than in (a)(c) is equal both in (a) and (b)

(d) none of the above

28. Moment of inertia of a uniform circular disc about a diameter

is I. Its moment of inertia about an axis ⊥ to its plane and

passing through a point on its rim will be

(a) 5I (b) 3I (c) 6I (d) 4I

29. The mean kinetic energy of a particle of mass m moving with

constant force in any interval of time will be …. where ω1

and ω2 are the initial and final velocities.

(a) )(6

m 2221

21 ω ω ω ω ++ (b)

221 )(

2

mω ω +

(c) 221 )(6m ω ω − (d) 221 )(

3m ω ω +

30. The rotational kinetic energy of a body is E and its moment

of inertia is 1. The angular momentum is

(a) EI (b) 2 IE

(c) EI 2 (d) E/I.

31. Three thin rods each of length L and mass M are placed along

X, Y and Z-axes in such a way that one end of each of the

rods is at the origin.

The moment of inertia of this system about Z-axis is :

(a)3

ML2 2

(b)3

ML4 2

(c)3

ML5 2

(d)3

ML2

32. Two discs, each of mass 1 kg and radius 2 metre, are

placed parallel to each other and separated by a distance o

2 metre.

YY’ is an axis which is perpendicular to the line joining

the centers of the two discs and is mid-way between the two

discs. The moment of inertia of the system about YY’ is

(a) 1 kg m2 (b) 2 kg m2

(c) 4 kg m2 (d) 8 mg r 12

33. Two thin discs each of mass M and radius r metre are

attached as shown in fig., to form a rigid body.

The rotational inertia of this body about an axis perpendicular to the plane of disc B and passing through its

centre is :

a) 2Mr 2 b) 3Mr 2

c) 4Mr 2 d) 5Mr 2

34. Two uniform thin identical rods AB and CD each of mass M

and length L are joined so as to form a cross as shown.

The moment of inertia of the cross about a bisector lineEF is :

(a)6

ML2

(b)4

ML2

(c)12

ML2

(d)3

ML2

35. When a ceiling fan is switched off, its angular velocity falls

to half while it makes 36 rotations. How many more rotations

will it make before coming to rest ? (Assume uniform angular

retardation)

(a) 36 (b) 24

(c) 18 (d) 12

C

D

A B

F

E

AB

Y

Y'

Z

Y

x

Wood Steel AO F

(a

Wood A/SteelO / F

b



36. The moment of inertia of a uniform thin rod of length

L and mass M about an axis passing through a point at

a distance of L/3 from one of its ends and

perpendicular to the rod is :

(a)48

ML7 2

(b)1

ML2

(c)

9

ML2

(d)

3

ML2

37. Two thin discs each of mass M and radius r metre are

attached as shown in fig., to form a rigid body. The

rotational inertia of this body about an axis

perpendicular to the plane of di sc B and passing

through its centre is :

(a) 2Mr 2 (b) 3Mr 2

(c) 4Mr 2 (d) 5Mr 2

38. A uniform disc of mass M and radius R is mounted on

an axle supported in frictionless bearings. A light cord

is wrapped around the rim of the disc and a steady

downward pull T is exerted on the cord. The angular

acceleration of the disc is :

(a) MR

T (b) T

MR

(c)MR

T2 (d)

T2

MR

39. A body is rolling without slipping on a horizontal

surface and its rotational kinetic energy is equal to the

translational kinetic energy. The body is :

(a) disc (b) sphere

(c) cylinder (d) ring

40. A particle is mass m is projected with a velocity v

making an angle of 45° with the horizontal. The

magnitude of angular momentum of the projectile

about an axis of projection when the particle is at

maximum height h is :

(a) zero (b)g24

mv3

(c)g2

mv2

(d) m 3gh2

41. A rigid body is made of three identical thin rods, each

of length L fastened together in the form of letter H.

The body is free to rotate about a horizontal axis that

runs along the length of one of the legs of the H. The

body is al lo wed to fa ll from rest from a position in

which the plane of H is horizontal. What is the angular

speed of the body when the plane of H is vertical ?

(a)L

g (b)

L

g

2

1

(c)L

g

2

3 (d) 2

L

g

42. A uniform rod of mass M and length L is pivoted at

one end such that it can rotate in a vertical plane

There is negligible friction at the pivot. The free endof the rod is held vertically above the pivot and then

released. The angular acceleration of the rod when it

makes an angle θ with the vertical is :

(a) g sin θ (b)l

gsin θ

(c)l2

g3 sin θ (d) 6 gl sin θ

43. A uniform cube of side a and mass m rests on a rough

horizontal table. A horizontal force F is applied

normal to one of the faces at a point that is directly

above the centre of face, at a height4

a3above the base

The minimum value of F for which the cube begins to

tilt about the edge is (assume that the cube does not

slide) :

(a)4

mg (b)

3

mg2

(c)4

mg3 (d) mg

44. A cubical block of mass M and edge a slides down a

rough inclined plane of inclination θ with a uniform

velocity. The torque of the normal force on the block

about its centre has a magnitude :

(a) zero (b) Mga

(c) Mga sin θ (d)2sinMga θ

45. A rigid spherical body is spinning around an axis

without any external torque. Due to change in

temperature, the volume increases by 1%. Its angular

speed :

(a) will increase approximately by 1%

(b) will decrease approximately by 1%

(c) will decrease approximately by 0.67%

(d) will decrease approximately by 0.33%

rotational motion

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