BANGLADESHPHYSICS OLYMPIAD

2016

CATEGORY "B"

Science Olympiad Blog

1. A piece of ice at 0 C is mixed with some water also at 0 C. If there is no heat exchange of the ice-/water mixture with the outside world, what will happen when the ice-water mixture reaches equilibrium? 0 C 0 C - -

? [2] 2. There is of water at in an aluminum calorimeter of mass . If an

aluminum rod of mass and temperature is dropped in it by what percentage of

the length will increase? [The specific heat of water= , the specific heat of

aluminum is and the coefficient of length expansion of aluminum, =

]

? [ ,

= ] [3]

3. In this picture three weights K, L and M are hanging with three spring scales D1, D2 and D3. The ratio of the values in those scales is D1: D2: D3 = 10:5:2.

a) If you swap the two weight K and M the summation of the values of three spring scale will increase about 4 kg. Find the values of each weights.

b) Now you put this system into a lift which is accelerating upward. If the value of acceleration is 2 m/s2. Find the ratio of the values in those scales.

c) If the lift is free falling again find the ratio of the values in those scales.

D1, D2 D3 K, L, M D1: D2: D3 = 10:5:2

a) K L 4 kg [3]

b) 2 m/s2 ? [1]

c) ? [1]

4. A wall is d = 9m length away from a lamp post. The height of the lamp post and the wall is H = 53 m and h= 3m respectively. Find the inclination () of the walls such that the shadow cast by the wall is longest. H= 53 m h = 3m d = 9m () ? [5] 5. The famous equation of Einstein, E = mc2 relates the mass of an object with its energy. But there is another more general expression which tells us the relationship between energy, mass and momentum. That is E2 = p2c2 + m2c4, here p is the momentum of the object, c is the speed of light in vacuum and m is the mass of the object. This expression holds for both matter and massless particles. So this expression of E contains all sorts of energies that can be incorporated in the object like potential energy, kinetic energy etc. Now in an experiment an atom at rest in a laboratory emits a photon and recoils. If its initial mass is m0 and it loses its mass which is equivalent to the energy Eloss in the emission, derive an expression for the frequency of the emitted photon using Eloss , m0, c and h. Here, h is Planks constant. (Hints. Use energy conservation law and Plancks law, E = hf where h is Planks constant, f is the frequency of the photon and E is the energy of the photon.) E = mc2 ,

E2 = p2c2 + m2c4, m , p , c

E ,

m0 Eloss Eloss , m0, c h h (Hints. , E = hf , h , f E ) [5] 6. A cylinder of length L is made by mixing two materials of density 1 and 2 .Their

density distribution varies along the density axis according to the following relation,

() = +

( )

When the cylinder is kept in a liquid of density 0 as shown in figure, x1 length is above

the liquid level. If the cylinder is rotated 1800, x2 length is above liquid level.

a) Find the relation between x1 and x2, for which the above condition is possible.

b) If the center of mass of the cylinder is located at L/3 position, find the 1 and 2 in terms of 0, x1, x2 and L.

L 1 2

,

() = +

( )

0

x1

1800

x2

a) x1 x2

b) L/3 ,

1 2 0, x1, x2 L

[10]

7. The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor, transverse to an electric current in the conductor and a magnetic field perpendicular to the current.

a) Find the relation between velocity of electron v and current I. b) Because of the magnetic force on the electron they move at the edge of the

conductor as shown in the figure and create a electrostatic force that opposes the

magnetostatic force. Find the expression for electrostatic force and magnetostatic

force when they balance each other. c) At equilibrium find an expression for Hall voltage VH in terms of magnetic field B,

electrons velocity v and width d. Now, in a Hall-effect experiment, a current of 3.0 A sent lengthwise through a conductor 1.0 cm wide, 4.0 cm long, and 10 mm thick produces a transverse (across the width) Hall potential difference of 10 mV when a magnetic field of 1.5 T is passed perpendicularly through the thickness of the conductor. From these data, find the number of electrons per unit volume of the conductor. [Hints. The magnetostatic force acting on a moving charge passing through uniform magnetic field is given by, F = qvB . Where, B = magnetic field strength (unit Tesla), v = velocity of charged particle that is perpendicular to the magnetic field lines. F is perpendicular to both velocity and magnetic field. ]

B , VH ( )

a) v I b) ( )

c) VH B,v,d B , v

d 4.0 cm , 1.0 cm 10 mm 3.0 A 1.5 T ,

, [ F = qvB q , v B F v B ] [10]

8. A student investigates the oscillation of a simple pendulum attached to a pole on the side of a building as shown in the figure below.

The student records the distance d from the ground to the center of the pendulum bob

and the time t for the pendulum to complete 10 oscillations. It is suggested that the

period T of the oscillations and the distance d are related by the equation

=

( )

Here g is the acceleration of free fall and k is a constant.

d 10 T

, d T

=

( )

g k

a) A graph is plotted of T2 on the y-axis against d on the x-axis. Determine

expressions for the gradient and the y-intercept in terms of g and k.

d x T2 y

g k

[1]

b) For each value of d the measurement of t is repeated. Values of d and t are given

in figure below. Calculate and record values of of mean t/s, T/s, T2/s2

d t d t t/s,

T/s, T2/s2 [2]

c) Plot a graph of T2/s2 against d/m. Include error bars for d.

T2/s2 d/m d error bars [2]

d) Draw the straight line of best fit and a worst acceptable straight line on your

graph. Both lines should be clearly labeled.

(best fit)

(

) [2]

e) Determine the gradient of the line of best fit. Include the uncertainty in your

answer.

Best fit [2]

f) Determine the y-intercept of the line of best fit. Include the uncertainty in your

answer.

Best fit

[ All the graphs has to be plotted in the graph paper given below] (

) [1]