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
a cosθ
4 a cos
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.
80 kg
The volume of the raft is given by
If the raft is immersed fully in water, then the weight of water displaced is
= Vdwater
= 0.2 × 103 = 200 kg
Hence, the additional weight which can be put on the raft
= 200 kg - 120 kg = 80 kg
A monoatomic gas supplied the heat Q very slowly keeping the pressure constant. The work done by the gas will be:
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