11.

A body of mass 2m is placed on earth's surface. Calculate the change in gravitational potential energy, if this body is taken from earth's surface to a height of h, where h = 4R.

• $\frac{2 \mathrm{mgh}}{\mathrm{R}}$

• $\frac{2}{3} \mathrm{mgR}$

• $\frac{8}{5} \mathrm{mgR}$

• $\frac{\mathrm{mgR}}{2}$

A solid sphere of mass M and radius 2 R rolls down an inclined plane of height h without slipping. The speed of its centre of mass when it reaches the bottom is

• $\sqrt{\frac{6}{7} \mathrm{gh}}$

• $\sqrt{3 \mathrm{gh}}$

• $\sqrt{\frac{10}{7} \mathrm{gh}}$

• $\sqrt{\frac{4}{3} \mathrm{gh}}$

A liquid of density 800 kg/m³ is filled in a cylindrical vessel upto a height of 3 m. This cylindrical vessel stands on a horizontal plane. There is a circular hole on the side of the vessel. What should be the minimum diameter of the hole to move the vessel on the floor, if plug is removed. Take the coefficient of friction between the bottom of the vessel and the plane as 0.5 and total mass of vessel plus vessel as 95 kg.

• 0.107 m

• 0.053 m

• 0.206 m

• 0.535 m

One mole of a monoatomic ideal gas undergoes the process A → B in the given p-V diagram. The molar heat capacity for this process is

• $\frac{3\mathrm{R}}{2}$

• $\frac{13 \mathrm{R}}{6}$

• $\frac{5 \mathrm{R}}{2}$

• 2R

A pan with a set of weights is attached to a light spring. The period of vertical oscillation is 0.5s. When some additional weights are put in pan, then the period of oscillations increases by 0.1 s. The extension caused by the additional weight is

• 5.5 cm

• 3.8 cm

• 2.7 cm

• 1.3 cm

The intensity of each of the two slits in Young's double slit experiment is I₀ Calculate the minimum separation between the points on the screen, where intensities are 2I₀ and I₀ If fringe width is b

• $\frac{\mathrm{b}}{5}$

• $\frac{\mathrm{b}}{8}$

• $\frac{\mathrm{b}}{12}$

• $\frac{\mathrm{b}}{4}$

A metal rod at a temperature of 145°C, radiates energy at a rate of 17W. If its temperature is increased to 273°C, then it will radiate at the rate of

• 49.6 W

• 17.5 W

• 50.3 W

• 67.5 W

A lead bullet penetrates into a solid object and melts. Assuming that 50% of its kinetic energy was used to heat it, the initial speed of the bullet is (the initial temperature of the bullet is 25^oC and its melting point is 300°C). Latent heat of fusion of lead= 2.5 x 10⁴ J/kg and specific heat capacity of lead= 125 J/kg-K

• 100 m/s

• ≈ 490 m/s

• 520 m/s

• 360 m/s

The temperature of a gas is raised from 27° C to 927° C. The root mean square speed

• gets halved

• gets doubled

• is $\left(\sqrt{\frac{927}{27}}\right)$ times the earlier value

• remains the same

A capillary tube of length L and radius r is connected with another capillary tube of the same length but half the radius in series. The rate of steady volume flow of water through first capillary tube under a pressure difference of p is V. The rate of steady volume flow
through the combination will be (the pressure difference across the combination is p)

• 17 V

• $\frac{16}{17} \mathrm{V}$

• $\frac{\mathrm{V}}{17}$

• $\frac{17}{16} \mathrm{V}$