A simple pendulum is vibrating in an evacuated chamber, it will oscillate with

A trolley of mass $m_1$ is placed on horizontal rigid pair of rails at same height. A mass $m_2$ is suspended to the trolley vertically by me ans of a ideal massless rope. The rope hangs between rails without touching them. Trolley can move along smooth rails but can't move in any other direction. Suspended mass is given small oscillation and perform $SHM$ after displacing small from stable equilibrium position in two ways, first perpendicular to the rails and second parallel to the rails. The ratio of time period of these (second case to first case) two $SHM's$ is

How many amplitudes of $SHO$ covers the distance in the half period ?

A simple pendulum is made of a body which is a hollow sphere containing mercury suspended by means of a wire. If a little mercury is drained off, the period of pendulum will

The metallic bob of simple pendulum has the relative density $5$. The time period of this pendulum is $10\,s$. If the metallic bob is immersed in water, then the new time period becomes $5 \sqrt{ x } s$. The value of $x$ will be.