21.

If at the same temperature and pressure, the densities of two diatomic gases are d1 and d, respectively, the ratio of mean kinetic energy per molecule of gases will be

• 1 : 1

• ${\mathrm{d}}_1$ : ${\mathrm{d}}_2$

• $\sqrt{{\mathrm{d}}_1} : \sqrt{{\mathrm{d}}_2}$

• $\sqrt{{\mathrm{d}}_2} : \sqrt{{\mathrm{d}}_1}$

A black body of mass 34.38 g and surface area 19.2 cm² is at an initial temperature of 400 K. It is allowed to cool inside an evacuated enclosure kept at constant temperature 300 K. The rate of cooling is 0.04${}^{°}\mathrm{C}$/s. The specific heat of the body is (Stefan's constant σ = 5.73 × 10^-8 Jm^-2K^-4)

• 2800 J/kg-k

• 2100 J/kg-k

• 1400 J/kg-K

• 1200 J/kg-K

A-pendulum suspended from the ceiling of a train has a period T when the train is at rest. When the train accelerates with a uniform acceleration a, the period of oscillation will

• increase

• decrease

• remain unaffected

• become infinite

The motion of a particle executing SHM is given by x = 0.01sin1O0$\mathrm{\pi }$(t + 0.05), where x is in metre and t in second. The time period of
motion (in second) is

• 0.01

• 0.02

• 0.1

• 0.2

When a certain volume of water is subjected to 100 kPa pressure, the volume of water decreases by 0.005%. The speed of sound in water must be

• 140 m/s

• 300 m/s

• 1400 m/s

• 5000 m/s

A man stands in a narrow, steep-sided valley. When he shouts he hears two echoes, one after 1s and other after 2s.If the velocity of sound in air is 330 m/s, the width of the valley is

• 330 m

• 495 m

• 660 m

• 990 m

A cylindrical tube, open at both ends emits a fundamental frequency f in air. The tube is dipped vertically in water, so that half of it is in water. The fundamental frequency of air column is now

• f/2

• 3f/4

• f

• 2f

The end correction of a resonance column is 1.0 cm. If the shortest length resonating with the tuning fork is 15.0 cm, the next resonating length will be

• 31 cm

• 45 cm

• 46 cm

• 47 cm

The breaking strength of a rod of diameter 2 cm is 2x 10⁵ N. Then that for rod of same material but diameter 4 cm will be

• 2 × 10⁵ N

• 1 × 10⁵ N

• 8 × 10⁵ N

• 0.5 × 10⁵ N

A metallic rod of Young's modulus 2x10¹¹ N/m² undergoes a strain of 0.5%. Then the energy stored per unit volume in the rod will be

• 2.5 × 10⁶ J/m³

• 5 × 10⁸ J/m³

• 2.5 × 10⁸ J/m³

• 0.5 × 10¹¹ J/m³