21.

A motor is rotating at a constant angular velocity of 600 rpm. The angular displacement per second is

• $\frac{3}{50 \mathrm{\pi }} \mathrm{rad}$

• $\frac{3\mathrm{\pi }}{50} \mathrm{rad}$

• $\frac{50 \mathrm{\pi }}{3} \mathrm{rad}$

• $\frac{3\mathrm{\pi }}{25} \mathrm{rad}$

If the mass of moon is $\frac{1}{90}$ of earth's mass, its radius is $\frac{1}{3}$ of earth's radius and if g is acceleration due to gravity on earth, then the acceleration due to gravity on moon is

• $\frac{\mathrm{g}}{3}$

• $\frac{\mathrm{g}}{90}$

• $\frac{\mathrm{g}}{10}$

• $\frac{\mathrm{g}}{9}$

A soap bubble in air (two surfaces) has surface tension 0.03 Nm^-1. Find the gauge pressure inside a bubble of diameter 30 mm.

• 2 Pa

• 4 Pa

• 8 Pa

• 10 Pa

A piece of ice is floating in a jar containing water. When the ice melts then the level of water

• rises

• falls

• remains unchanged

• rises or falls

A 10 cm³ cube floats in water with a height of 4 cm³ remaining above the surface. The density of the material from which the cube is made is

• 0.6 g cm^-3

• 1.0 g cm^-3

• 0.4 g cm^-3

• 0.24 g cm^-3

Compressibility of water is 5 × 10^-10 m²/N. The change in volume of 100 mL water subjected to 15 × 10⁶ Pa pressure will

• no change

• increase by 0.75 mL

• decrease by 0.75 mL

• increase by 1.50 mL

A wire of length L and area of cross-section A is stretched through a distance x metre by applying a force F along length, then the work done in this process is : (Y is Young's modulus of the material)

• $\frac{1}{2} \left(\mathrm{A} . \mathrm{L}\right) \left(\frac{\mathrm{Yx}}{\mathrm{L}}\right) \left(\frac{\mathrm{x}}{\mathrm{L}}\right)$

• $\left(\mathrm{A} . \mathrm{L}\right) \left(\mathrm{YL}\right) \left(\frac{\mathrm{x}}{\mathrm{L}}\right)$

• $2 \left(\mathrm{A} . \mathrm{L}\right) \left(\mathrm{YL}\right) \left(\frac{\mathrm{x}}{\mathrm{L}}\right)$

• $3 \left(\mathrm{A} . \mathrm{L}\right) \left(\mathrm{YL}\right) \left(\frac{\mathrm{x}}{\mathrm{L}}\right)$

Which of the accompanying P-V diagrams best represents an isothermal process ?

800 cc volume of a gas having $\mathrm{\gamma } = \frac{5}{3}$ is suddenly compressed adiabatically to 100 cc. If the initial pressure is P, then the final pressure will be

• $\frac{\mathrm{P}}{32}$

• $\left(\frac{24}{5}\right) \mathrm{P}$

• 8 P

• 32 P

An ice box made of Styrofoam (Thermal conductivity = 0.01 Jm^-1 s^-1 K^-1) is used to keep liquids cool. It has a total wall area including lid of 0.8 m² and wall thickness of 2.0cm. A bottle of water is placed in box and filled with ice. If the outside temperature is 30°C, the rate of flow of heat into the box is ( in J s^-1)

• 16

• 14

• 12

• 10