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

If g is the acceleration due to gravity on the earth s surface, the gain in potential energy of the
body at a height equal to two times the radius R of the earth will be:

The moment of inertia of a uniform horizontal cylinder of mass M about an axis passing
through its edge and perpendicular to the axis of the cylinder when its length is 6 times its
radius R is

Two soap bubbles of radii x and y coalesce to constitute a bubble of radius z is equal
to

A particle of mass m is located in a one dimensional potential field where potential
energy is given by:
V(x) = A(1 – cos px), where A and p are constants. The period of small oscillations of the particle is

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 a, is given by

A diver at a depth of 12 m in water $\\mu=\\dfrac{4}{3}$ sees the sky in a cone of semiverticale
angle :

A particle performs a uniform circular motion with an angular momentum L. If the frequency of
the particle s motion is doubled and its KE is halved, the angular momentum becomes

A radioactive substance has a half-life of 60 minutes. During 3 hour, the fraction of atoms that
have decayed would be

A convex lens of focal length 30 cm produces 5 times magnified real image of an
object. What is the object distance ?