The displacement of a particle is given by the relation $x=4(\cos \pi t+\sin \pi t)$. The amplitude of the particle is

A body of mass $m$ is at height $R$ from the surface of the earth where $R$ is the radius of the earth. If the body is taken from here to a height of $3 R$ from the surface of the earth, the increase in the gravitational potential energy of the body is

( $g$ is acceleration due to gravity on the surface of the earth)

The ratio of the areas of cross-sections of three wires is $1: 2: 3$ and the ratio of the Young's modulii of their materials is $3: 2: 1$. If the three wires are of same length and same stretching force is applied to the three wires, then the ratio of the elongations of the three wires is

When a large bubble rises from the bottom of a lake to the surface, the volume of the bubble becomes 5 times its volume at the bottom of the lake. If $H$ is the atmospheric pressure expressed in terms of water column height, then the depth of the lake is

(The temperature of the water in the lake is same at all points)