Two solid conducting sphere of radius $10$ $cm$ and $20$ $cm$ having $5×10^{-6}$ $C$

and $30×10^{-6}$ $C$ respectively are kept at $2$ meter distance.Then they are connected by a conducting wire.Find the amount of heat generated in this process.

Problem 2.

A bomb has just burst at the ground.Let the particle of the bomb acquires a constant speed $20$ $m$ $s^{-1}$.What would be the area the particles will cover?

Problem 3.

Two prisms make a cube as shown in in the picture.The first prism has a refraction index $\mu_1=1.5$ and the second prism has a unknown refraction index $\mu_2$.Light enters the cube perpendicular and leaves the cube parallel to the other side.Find the equation of $\mu_2$.

(The equation may be complicated.Just find the equation that can be solved to find $\mu_2$ )

Problem 4.

Lily is in a spaceship moving at speed $V=0.5c$ with respct to a viewer at rest on earth. Her friends james and severus are also in their own spaceships.Lily is watching that Severus is going forward at a speed $V_1=0.8c$ and James is going backward at a speed $V_2=0.85c$.

How fast is James going according to Severus?

Problem 5.

An ice cube of volume $V$ mass $m$ is placed onto water.When the cube is pressed slightly off-centered into the water it begins to oscillate.Find the angular frequency of the oscillation.

(The density of water is $P$).

Problem 6.

Gautum must have made a calculation mistake somewhere .In his calculation of the efficiency of the heat engine,he created,he has derived the expression $e=(T_H+T_C)/(T_H+2T_C)$.$T_H$ is temparature of heat source and $T_C$ is temparature of cold sink.

State the law of thermodynamics that this expression violates,and explain why.

Problem 7..

**Birth of a Supernova**.

A spherical star of mass $M$ and radius $R$ isin a final step to be a supernova.In this process the star produce a large ammount of heat energy.As a result,the size of the star increases rapidly.Let assume the readius of the star becomes $100R$ .For simplicity we assume that density is uniform all the time.

(a)Find the total energy of the star at the initial and the final condition.

(b)Find the heat energy produced by the star.Let the star radiates heat exponentially as $E(y)=Ae^{-y} $.[Here $E(y)$ is the radiation rate at year $y$ ] It takes $y$ year to radiate all the energy produced. (when it was becoming a supernova)

(c) Find $A$.

**Note**