A stone of relative density K is released from rest on the surface ofa lake. If viscous effects are ignored, the stone sinks in water with an acceleration of
g (1 − K)
g (1 + K)
A material has Poisson's ratio 0.50. If a uniform rod of it suffers a longitudinal strain of 2 x 10-3 , then the percentage change in volume is
0.6
0.4
0.2
zero
Two identical springs are connected to mass m as shown (k = spring constant). If the period of the configuration in (a) is 2s, the period of the configuration in (b) is
1 s
An object weights m1 in a liquid of density d1 and that in liquid of density d2 is m2. The density d of the object is
A body floats in water with 40% of its volume outside water. When the same body floats in an oil. 60% of its volume remains outside oil. The relative density of oil is
0.9
1.0
1.2
1.5
Two soap bubbles of radii x and y coalesce to constitute a bubble of radius z. Then z is equal to
x + y
A particle of mass m is located in a one dimensional potential field where potential energy is given by V(x) = A(l − cos px), where A and p are constants. The period of small oscillations of the particle is
B.
We are given that a particle of mass m is located in a one dimensional potential field and the potential energy is given by V(x) = A(1 − cos px). So, we can find the force experienced by the particle as
For small oscillations, we have
F ≈ − Ap2x
Hence, the acceleration would be given by
Also we know that
The period of oscillation of a simple pendulum of length l suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination α is given by
A plane progressive wave is given by y = 2 cos 6.284 (330t − x). What is the period of the wave ?
The displacement of a particle is SHM varies according to the relation x = 4 (cos πt + sin πt). The amplitude of the particle is
− 4
4
8