31.

A capillary tube of radius 0.5 mm is immersed in a beaker of mercury. The level inside the tube is 0.8 cm below the level in beaker and angle of contact is 120°. What is the surface tension of mercury, if the mass density of mercury is ρ = 13.6 x10³ kgm^-3 and acceleration due to gravity is g = 10 m/s² ?

• 0.225 N/m

• 0.544 N/m

• 0.285 N/m

• 0.375 N/m

Which of the following statement related to stress-strain relation is correct ?

• Stress is linearly proportional to strain irrespective of the magnitude of the strain

• Stress is linearly proportional to strain above

• Stress is linearly proportional to strain for stress much smaller than at the yield point

• Stress-strain curve is same for all materials

The lower edge of a square slab of side 50 cm and thickness 20 cm is rigidly fixed to the base of a table. A tangential force of 30 N is applied to the slab. If the shear moduli of the material is 4 x 10¹⁰ N/m², then displacement of the upper edge, in meters is

• 4 × 10^-12

• 4 × 10^-10

• 6 × 10^-10

• 6 × 10^-12

Initially a beaker has 100 g of water at temperature 90°C. Later another 600 g of water at temperature 20°C was poured into the beaker. The temperature, T of the water after mixing is

• 20°C

• 30°C

• 45°C

• 55°C

Match the following

• I-4, II-3, III-2, IV-1

• I-3, II-2, III-1, IV-4

• I-1, II-2, III-3, IV-4

• I-4, II-2, III-3, IV-1

For an ideal gas, the specific heat at constant pressure C_p is greater than the specific heat at constant volume C_v. This is because

• There is a finite work done by the gas on its environment when its temperature is increased while the pressure remains constant

• There is a finite work done by the gas on its environment when its pressure is increased while the volume remains constant

• There is a finite work done by the gas on its environment when its pressure is increased while the temperature remains constant

• The pressure of the gas remains constant when its temperature remains constant

Which of the following statement is correct ?

• Light waves are transverse but sound waves are waves on strings are longitudinal

• Sound waves and waves on a string and transverse but light waves are longitudinal

• Light waves and waves on a string are transverse but sound waves are longitudinal

• Light waves and sound waves are transverse but waves on string are longitudinal

The phase velocity of a wave described by the equations  is

• x/t

• ψ₀/ω

• ω/k

• $\mathrm{\pi }/2\mathrm{k}$

Wavelength of the wave with 30 MHz frequency is

• 1 cm

• 10 cm

• 100 cm

• 1000 cm

A copper wire with a cross-section area of 2 x10^-6 m² has a free electron density equal to 5 x 10²² /cm³. If this wire carries a current of 16 A, the drift velocity of the electron is

• 1 m/s

• 0.1 m/s

• 0.01 m/s

• 0.001 m/s