31.

Find the increase in pressure required to decrease the volume of water sample by 0.01%. Bulk modulus of water = 2.1 × 10⁹ Nm^-2 .

• 4.3x 10⁴ N/m²

• 1.8 × 10⁷ N/m² 

• 2.1 × 10⁵ N/m²

• 3.7 × 10⁴ N/m²

Figure shows spring + block + pulley system which are light. The time period of mass would be

• $2\mathrm{\pi } \sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$

• $\frac{1}{2\mathrm{\pi }}\sqrt{\frac{\mathrm{k}}{\mathrm{m}}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$

• $\frac{1}{2\mathrm{\pi }} \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$

The given p-V diagram shows gases during adiabatic process. Plots 1 and 2 should correspond respectively to

• He and O₂

• O₂ and He

• He and Ar

• O₂ and N₂

For an adiabatic expansion of a monoatomic perfect gas, the volume increases by 24%. What is the percentage decrease in pressure?

• 24%

• 40%

• 48%

• 71%

A slab consists of portions of different materials of same thickness and having the conductivities K₁ and K₂. The equivalent thermal conductivity of the slab is

• K₁ + K₂

• $\sqrt{{\mathrm{K}}_1 + {\mathrm{K}}_2}$

• $\frac{2 {\mathrm{K}}_1 {\mathrm{K}}_2}{{\mathrm{K}}_1 + {\mathrm{K}}_2}$

• $\sqrt{\frac{{\mathrm{K}}_1 {\mathrm{K}}_2}{{\mathrm{K}}_1+ {\mathrm{K}}_2}}$

Two rigid boxes containing different ideal gases are placed on table. Box A contains one mole of nitrogen at temperature T₀ , while box B contains 1 mole of helium at temperature 7/3 T₀. The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes) then the final temperature of gases, T_f in terms of T₀ is

• $\frac{2\hspace{0.17em}{\mathrm{T}}_0}{5}$

• $\frac{3 {\mathrm{T}}_0}{5}$

• $\frac{5 {\mathrm{T}}_0}{3}$

• $\frac{9 {\mathrm{T}}_0}{7}$

The temperature of the cold junction of thermocouple is 0°C and the temperature of hot junction is T^o C. The emf is E = 16T - 0.04T² µV. The inversion temperature T_f is

• 300^o C

• 200^o C

• 500^o C

• 400^o C

Two long straight wires, each carrying an electric current of 5 A, are kept parallel to each other at a separation of 2.5 cm. Find the magnitude of the magnetic force experiment by 10 cm of a wire.

• 4.0 × 10^-4 N

• 3.5 × 10^-6 N

• 2.0 × 10^-5 N

• 2.0 × 10^-9 N

A wire of resistance 10Ω is bent to form a complete circle. Find its resistance between two diametrically opposite point.

• 5 Ω

• 2.5 Ω

• 1.25 Ω

• $\frac{10}{3}$ Ω

Find the resistance of a hollow cylindrical conductor of length 1.0 mm and 2.0 mm respectively. The resistivity of the material is 2.0 × 10^-8 Ωm

• 2.1 × 10^-3 Ω

• 1.3 × 10^-4 Ω

• 3.2 × 10^-4 Ω

• 4.6 × 10^-2 Ω