11.

A uniform solid spherical ball is rolling down a smooth inclined plane from a height h. The velocity attained by the ball when it reaches the bottom of the inclined plane is v. If the ball is now thrown vertically upwards with the same velocity v, the maximum height to which the ball will rise is

• $\frac{5\mathrm{h}}{8}$

• $\frac{3\mathrm{h}}{5}$

• $\frac{5\mathrm{h}}{7}$

• $\frac{7\mathrm{h}}{9}$

If n denotes a positive integer, h the Planck's constant, q the charge and B the magnetic field, then the quantity $\left[\frac{\mathrm{nh}}{2\mathrm{\pi qB}}\right]$ has the dimension of

• area

• length

• speed

• acceleration

Consider a black body radiation in a cubical box at absolute temperature T. If the length of each side of the box is doubled and the temperature of the walls of the box and that of the radiation is halved, then the total energy

• halves

• doubles

• quadruples

• remains the same

A solid uniform sphere resting on a rough horizontal plane is given a horizontal impulse directed through its centre so that it starts sliding with an initial velocity v₀. When it finally starts rolling without slipping the speed of its centre is

• $\frac{2}{7} {\mathrm{v}}_0$

• $\frac{3}{7} {\mathrm{v}}_0$

• $\frac{5}{7} {\mathrm{v}}_0$

• $\frac{6}{7} {\mathrm{v}}_0$

Three identical square plates rotate about the axes shown in the figure in such a way that their kinetic energies are equal. Each of the rotation axes passes through the centre of the square. Then the ratio of angular speeds ω₁ : ω₂ : ω₃ is

• 1 : 1 : 1

• $\sqrt{2} : \sqrt{2} : 1$

• $1 : \sqrt{2} : 1$

• $1 : 2 : \sqrt{2}$

A thin rod AB is held horizontally so that it can freely rotate in a vertical plane about the end A as shown in the figure. The potential energy of the rod when it hangs vertically is taken to be zero. The end B of the rod is released from rest from a horizontal position. At the instant the rod makes an angle θ with the horizontal

• the speed of end B is proportional to $\sqrt{\sin \mathrm{\theta }}$

• the potential energy is proportional to (1 − cos θ)

• the angular acceleration is proportional to cos θ

• the torque about A remains the same as its initial value

A whistle whose air column is open at both ends has a fundamental frequency of 5100 Hz. If the speed of sound in air is 340 ms^-1, the length of the whistle, in cm, is

• 5/3

• 10/3

• 5

• 20/3

One mole of an ideal monoatomic gas is heated at a constant pressure from 0°C to 100°C. Then the change in the internal energy of the gas is (Given, R = 8.32 J mol^-1 K^-1)

• 0.83 × 10³ J

• 4.6 × 10³ J

• 2.08 × 10³ J

• 1.25 × 10³ J

When a particle executing SHM oscillates with a frequency v, then the kinetic energy of the particle

• changes periodically with a frequency of v

• changes periodically with a frequency of 2v

• changes periodically with a frequency of v/2

• remains constant

A small metal sphere of radius a is falling with a velocity v through a vertical column of a viscous liquid. If the coefficient of viscosity of the liquid is η, then the sphere encounters an opposing force of

• $6{\mathrm{\pi \eta a}}^2\mathrm{v}$

• $\frac{6\mathrm{\eta v}}{\mathrm{\pi a}}$

• $6\mathrm{\pi \eta av}$

• $\frac{\mathrm{\pi \eta v}}{6{\mathrm{a}}^3}$