The modulus of elasticity is dimensionally equivalent to

• strain

• force

• stress

• coefficient of viscosity

Radius of an air bubble at the bottom of the lake is r and it becomes 2r when the air bubble rises to the top surface of the lake. If P cm of water be the atmospheric pressure, then the depth of the lake is

• 2P

• 8P

• 4P

• 7P

A manometer connected to a closed tap reads 4.5 × 10⁵ Pa. When the tap is opened the reading of the manometer falls to 4 x 10⁵ Pa. Then the velocity of flow of water is

• 7 ms^-1

• 8 ms^-1

• 10 ms^-1

• 12 ms^-1

What is the velocity v of a metallic ball of radius r falling in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body ? (The densities of metal and of liquid are ρ and σ respectively, and the viscosity of the liquid is η)

• $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }} \left(\mathrm{\rho } - 2\mathrm{\sigma }\right)$

• $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }} \left(2\mathrm{\rho } - \mathrm{\sigma }\right)$

• $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }} \left(\mathrm{\rho } - \mathrm{\sigma }\right)$

• $\frac{2{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }} \left(\mathrm{\rho } - \mathrm{\sigma }\right)$

The value of $\frac{\mathrm{PV}}{\mathrm{T}}$ for one mole of an ideal gas is nearly equal to

• 2 J mol^-1 K^-1

• 8.3 mol^-1 K^-1

• 4.2 mol^-1 K^-1

• 2 cal mol^-1 K^-1

The volume of a metal sphere increases by 0.24 % when its temperature is raised by 40°C. The coefficient of linear expansion of the metal is 

• 2 × 10^-5

• 6 × 10^-5

• 18 × 10^-5

• 1.2 × 10^-5

27.

The temperature of equal masses of three different liquids A, B and C are 12°C, 19°C and 28°C respectively. The temperature when A and B are mixed is 16°C and when B and C are mixed is 23°C. The temperature when A and C are mixed is

• 18.2°C

• 22°C

• 20.2°C

• 24.2°C

The time period of the second's hand of a watch is

• 1 h

• 1 s

• 12 h

• 1 min

A particle starts SHM from the mean position. Its amplitude is a and total energy E. At one instant its kinetic energy is $3\frac{\mathrm{E}}{4}$. Its displacement at that instant is

• $\frac{\mathrm{a}}{\sqrt{2}}$

• $\frac{\mathrm{a}}{2}$

• $\frac{\mathrm{a}}{\sqrt{\left({\displaystyle \frac{3}{2}}\right)}}$

• $\frac{\mathrm{a}}{\sqrt{3}}$

A particle executes linear simple harmonic motion with an amplitude of 2 cm. When the particle is at 1 cm from the mean position the magnitude of its velocity is equal to that of its acceleration. Then its time period in second is

• $\frac{1}{2\mathrm{\pi }\sqrt{3}}$

• $2\mathrm{\pi }\sqrt{3}$

• $\frac{2\mathrm{\pi }}{\sqrt{3}}$

• $\frac{\sqrt{3}}{2\mathrm{\pi }}$