A train is moving at 30 ms^-1 in still air. The frequency of the locomotive whistle is 500 Hz and the speed of sound is 345 ms^-1. The apparent wavelength of sound in front of and behind the locomotive are respectively

• 0.80 m, 0.63 m

• 0.63 m, 0.80 m

• 0.50 m, 0.85 m

• 0.63 m, 0.75 m

An open organ pipe is closed suddenly with the result that the second overtone of the closed pipe is found to be higher in frequency by 100 than the first overtone of the original pipe. Then the fundamental frequency of the open pipe is 

• 200 s^-1

• 100 s^-1

• 300 s^-1

• 250 s^-1

A transverse wave is described by the equation $\mathrm{y} = {\mathrm{y}}_0 \sin 2\mathrm{\pi } \left(\mathrm{ft} - \frac{\mathrm{x}}{\mathrm{\lambda }}\right)$. The maximum particle velocity is equal to four times the wave velocity, if

• $\mathrm{\lambda } = \frac{{\mathrm{\pi y}}_0}{4}$

• $\mathrm{\lambda } = \frac{{\mathrm{\pi y}}_0}{2}$

• $\mathrm{\lambda } = {\mathrm{\pi y}}_0$

• $\mathrm{\lambda } = 2{\mathrm{\pi y}}_0$

A simple pendulum is released from A as shown. If m and l represent the mass of the bob and length of the pendulum, the gain in kinetic energy at B is

• $\frac{\mathrm{mgl}}{2}$

• $\frac{\mathrm{mgl}}{\sqrt{2}}$

• $\frac{\sqrt{3}}{2} \mathrm{mgl}$

• $\frac{2}{\sqrt{3}} \mathrm{mgl}$

A tank of height H is fully filled with water. If the water rushing from a hole made in the tank below the free surface, strikes the floor at maximum horizontal distance, then the depth of the hole from the free surface must be

• $\left(\frac{3}{4}\right) \mathrm{H}$

• $\left(\frac{2}{3}\right) \mathrm{H}$

• $\left(\frac{1}{4}\right) \mathrm{H}$

• $\left(\frac{1}{2}\right) \mathrm{H}$

The length of a rubber cord is 11 metre when the tension is 4 N and l₂ metre when the tension is 6 N. The length when the tension is 9 N, is

• (2.5 l₂ − 1.5 l₁) m

• (6 l₂ − 1.5 l₁) m

• (3 l₂ − 2 l₁) m

• (3.5 l₂ − 2.5 l₁) m

27.

A wire of natural length l, Young's modulus Y and area of cross-section A is extended by x. Then the energy stored in the wire is given by

• $\frac{1}{2} \frac{\mathrm{YA}}{\mathrm{l}} {\mathrm{x}}^2$

• $\frac{1}{3} \frac{\mathrm{YA}}{\mathrm{l}} {\mathrm{x}}^2$

• $\frac{1}{2} \frac{\mathrm{Yl}}{\mathrm{A}} {\mathrm{x}}^2$

• $\frac{1}{2} \frac{\mathrm{YA}}{{\mathrm{l}}^2} {\mathrm{x}}^2$

A piece of solid weighs 120 g in air, 80 g in water and 60 g in a liquid. The relative density of the solid and that of the liquid are respectively

• 3, 2

• $2, \frac{3}{4}$

• $3, \frac{3}{2}$

• 4, 3

A closed gas cylinder is divided into two parts by a piston held tight. The pressure and volume of gas in two parts respectively are (p, 5V) and (l0p, V). If now the piston is left free and the system undergoes isthermal process, then the volume of the gas in two parts respectively are 

• $\frac{10}{11} \mathrm{V}, \frac{20}{11} \mathrm{V}$

• 3 V, 3 V

• 5 V, V

• 4 V, 2 V

A Carnot engine with sink's temprature at 17°C has 50% efficiency. By how much should its source temperature be changed to increase its efficiency to 60%

• 225 K

• 128°C

• 580 K

• 145 K