A bat flies at a steady speed of 4 ms^-1 emitting a sound of f =90 x 10³  Hz. It is flying horizontally towards a vertical wall. The frequency of the reflected sound as detected by the bat will be (take velocity of sound in air is 330 ms^-1)

• 88.1 × 10³ Hz

• 87.1 × 10³ Hz

• 92.1 × 10³ Hz

• 89.1 × 10³ Hz

A closed organ pipe and an open organ pipe of same length produce 2 beats/second while vibrating in their fundamental modes. The length of the open organ pipe is halved and that of closed pipe is doubled. Then the number of beats produced per second while vibrating in the fundamental mode is

• 2

• 6

• 8

• 7

13.

A uruform wire of length L, diameter D and density ρ is stretched under a tension T. The correct relation between its fundamental frequency f, the length L and the diameter D is

• $\mathrm{f} \propto \frac{1}{\mathrm{LD}}$

• $\mathrm{f} \propto \frac{1}{\mathrm{L}\sqrt{\mathrm{D}}}$

• $\mathrm{f} \propto \frac{1}{{\mathrm{D}}^2}$

• $\mathrm{f} \propto \frac{1}{{\mathrm{LD}}^2}$

Which of the following substances has the highest elasticity ?

• Sponge

• Steel

• Rubber

• Copper

Three liquids of equal masses are taken in three identical cubical vessels A, B and C. Their densities are ρ_A, ρ_B and ρ_C respectively but ρ_A < ρ_B < ρ_C . The force exerted by the liquid on the base of the cubical vessel is

• maximum in vessel C

• minimum in vessel C

• the same in all the vessels

• maximum in vessel A

Water is in streamline flows along a horizontal pipe with non-uniform cross-section. At a point in the pipe where the area of cross-section is 10 cm², the velocity of wateris 1 ms^-1 and the pressure is 2000 Pa. The pressure at another point where the cross-sectional area is 5 cm² is

• 4000 Pa

• 2000 Pa

• 1000 Pa

• 500 Pa

The temperature of a gas contained in a closed vessel of constant volume increases by 1°C when the pressure of the gas is increased by 1%. The initial temperature of the gas is

• 100 K

• 273°C

• 100°C

• 200 K

Two slabs are of the thicknesses d₁ and d₂. Their thermal conductivities are K₁ and K₂ respectively. They are in series. The free ends of the combination of these two slabs are kept at temperatures θ₁ and θ₂. Assume θ₁ > θ₂. The temperature θ of their common junction is

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

• $\frac{{\mathrm{K}}_1{\mathrm{\theta }}_1{\mathrm{d}}_1 + {\mathrm{K}}_2{\mathrm{\theta }}_2{\mathrm{d}}_2}{{\mathrm{K}}_1{\mathrm{d}}_2 + {\mathrm{K}}_2{\mathrm{d}}_1}$

• $\frac{{\mathrm{K}}_1{\mathrm{\theta }}_1{\mathrm{d}}_2 + {\mathrm{K}}_2{\mathrm{\theta }}_2{\mathrm{d}}_1}{{\mathrm{K}}_1{\mathrm{d}}_2 + {\mathrm{K}}_2{\mathrm{d}}_1}$

• $\frac{{\mathrm{K}}_1{\mathrm{\theta }}_1 \hspace{0.17em}+ {\mathrm{K}}_2{\mathrm{\theta }}_2}{{\mathrm{K}}_1 + {\mathrm{K}}_2}$

Hot water cools from 60°C to 50°C in the first 10 min and to 42°C in the next 10 min. Then the temperature of the surroundings is

• 20°C

• 30°C

• 15°C

• 10°C

The efficiency of Carnot's heat engine is 0.5 when the temperature of the source is T₁ and that of sink is T₂. The efficiency of another Carnot's heat engine is also 0.5. The temperatures of source and sink of the second engine are respectively

• 2T₁, 2T₂

• $2{\mathrm{T}}_1 ,\frac{{\mathrm{T}}_2}{2}$

• T₁ + 5, T₂ − 5

• T₁ + 10, T₂ − 10