Instructions

For the following questions answer them individually

Question 1

A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and sameradiusis also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation $$(\frac{E_{sphere}}{E_{cylinder}})$$ will be:

Question 2

A light rod of length l has two masses $$m_1$$ and $$m_2$$ attatched to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the center of mass is

Question 3

Starting from the centre of the earth having radius R, the variation of g (accelaration) due to gravity) is shown by

Question 4

A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. The total energy of the satellite in terms of $$g_0$$, the value of acceleration due to gravity at the earth's surface, is

Question 5

A rectangular film of liquid is extended from $$(4cm\times2cm)$$ to $$(5cm\times4cm)$$. If the work done is $$3\times10^{-4}$$ J, the value of the surface tension of the liquid is

Question 6

Three liquids of densities $$p_1,p_2$$ and $$p_3$$ (with $$p_1>p_2>p_3$$ ), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact $$\theta_1,\theta_2$$ and $$\theta_3$$ obey

Question 7

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at $$100^\circ C$$, while the other one is at $$0^\circÂ C$$. If the two bodies are brought into contact, then, assuming no heat loss, the final common temperature is

Question 8

A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newtonâ€™s law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be

Question 9

One mole of an ideal monatomic gas undergoes a process described by the equation $$PV^3$$ = constant. The heat capacity of the gas during this process is

Question 10

The temperature inside a refrigerator is $$t_{2}^0c$$ and the room temperature is $$t_{1}^0c$$. The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be