A particle is executing the motion x = a cos (ωt - θ). The maximum velocity of the particle is :

• aω cosθ

• aω

• aω sinθ

• none of these

A particle is executing two different simple harmonic motions, mutually perpendicular, of different amplitudes and having a phase difference of π/2. The path of the particle will be :

• circular

• straight line

• parabolic

• elliptical

Equations of motion in the same direction are given by :

y₁ = 2a sin(ωt - kx)

y₂ = 2a sin(ωt - kx - θ)

The amplitude of the medium particle will be:

• 2a cosθ

• $\sqrt{2}$ a cosθ

• 4 a cos$\frac{\mathrm{\theta }}{2}$

• $\sqrt{2}\mathrm{a} \cos \frac{\mathrm{\theta }}{2}$

24.

A closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. What is the ratio of their lengths?

• 1 : 2

• 2 : 1

• 2 : 3

• 4 : 3

A steel scale measures the length of a copper wire as 80.0 cm when both are at 20°C, the calibration temperature for the scale. What would the scale read for the length of the wire when both are at 40°C?

Given : α for steel = 11 × 10^-6 per °C and for Cu= 17 × 10^-6 per °C :

• 80.0096 cm

• 80.0272

• 1 cm

• 25.2 cm

A tank is filled with water upto height H. When a hole is made at a distance h below the level of water, what will be the horizontal range of water jet?

• 2√h(H - h)

• 4√h(H + h)

• 4√h(H - h)

• 2√h(H + h)

A raft of wood of mass 120 kg floats in water. The weight that can be put on the raft to make it just sink should be (draft = 600 kg/m³) :

• 80 kg

• 50 kg

• 60 kg

• 30 kg

A monoatomic gas supplied the heat Q very slowly keeping the pressure constant. The work done by the gas will be:

• $\frac{2}{3}\mathrm{Q}$

• $\frac{3}{5}\mathrm{Q}$

• $\frac{2}{5}\mathrm{Q}$

• $\frac{1}{5}\mathrm{Q}$

The temperature of the black body increases from T to 2T. The factor by which the rate of emission will increase is

• 4

• 2

• 16

• 8

In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is 0.17 sec. The frequency of the wave is :

• 1.47 Hz

• 2.94 Hz

• 0.73 Hz

• 0.36 Hz