A particle of mass m carrying charge q is kept at rest in a uniform electric field E and then released. The kinetic energy gained by the particle, when it moves through a distance y is

• $\frac{1}{2} {\mathrm{qEy}}^2$

• qEy

• qEy²

• qE²y

A small spherical ball falling through a viscous medium of negligible density has terminal velocity v. Another ball of the same mass but of radius twice that of the earlier falling through the same viscous medium will have terminal velocity

• v

• v/4

• v/2

• 2v

The excess pressure inside a spherical drop of water is four times that of another drop. Then their respective mass ratio is

• 1 : 16

• 8 : 1

• 1 : 4

• 1 : 64

In a capillary rise experiment, the water level rises to a height of 5 cm. If the same capillary tube is placed in water such that only 3 cm of the tube projects outside the water level, then

• water will begin to overflow through the capillary

• angle of contact decreases

• angle of contact increases

• the meniscus completely vanishes

The Young's modulus of the material of a wire is 2 × 10¹⁰ Nm^-2. If the elongation strain is 1 %, then the energy stored in the wire per unit volume in Jm^-3 is

• 10⁶

• 10⁸

• 2 × 10⁶

• 2 × 10⁸

The change in internal energy of a given mass of gas, when its volume changes from V to 2V at constant pressure p is $\left(\frac{{\mathrm{C}}_{\mathrm{p}}}{{\mathrm{C}}_{\mathrm{V}}} = \mathrm{\gamma }, \mathrm{universal} \mathrm{gas} \mathrm{constant} = \mathrm{R}\right)$

• $\frac{\mathrm{pV}}{\mathrm{\gamma }}$

• $\frac{\mathrm{pV}}{\left(2\mathrm{\gamma } - 1\right)}$

• $\frac{\mathrm{pV}}{\left(\mathrm{\gamma } -1\right)}$

• $\frac{\mathrm{R}}{\left(\mathrm{\gamma } - 1\right)}$

In a Carnot engine, the temperature of reservoir is 927°C and that of sink is 27°C. If the work done by the engine when it transfers heat from reservoir to sink is 12.6 x 10⁶ J, the quantity of heat absorbed by the engine from the reservoir is

• 16.8 × 10⁶ J

• 4 × 10⁶ J

• 7.6 × 10⁶ J

• 4.25 × 10⁶ J

In the given p-V diagram, I is the initial state and F is the final state.

The gas goes from I to F by

(i) IAF      (ii) IBF          (iii) ICF

The heat absorbed by gas is

• the same in all three processes

• the same in (i) and (ii)

• greater in (i) than in (ii)

• the same in (i) and (iii)

Hot water cools from 60°C to 50°C in the first 10 min and to 42°C in the next 10 min. The temperature of the surroundings is

• 10°C

• 5°C

• 15°C

• 20°C

30.

In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is 0.14 s. The frequencv of the wave is

• 0.42 Hz

• 2.75 Hz

• 1.79 Hz

• 0.56 Hz