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

What is the velocity of the bob of a simple pendulum at its mean position, if it is able to rise to vertical height of $10cm$  ……… $m/s$ (Take $g = 9.8\,m/{s^2})$

A heavy small-sized sphere is suspended by a string of length $l$. The sphere rotates uniformly in a horizontal circle with the string making an angle $\theta $ with the vertical. Then the time period of this conical pendulum is

Time period of a simple pendulum in a stationary lift is ' $T$ '. If the lift accelerates with $\frac{ g }{6}$ vertically upwards then the time period will be …..

(where $g =$ acceleration due to gravity)

A pendulum is suspended in a lift and its period of oscillation when the lift is stationary is  $T_0$. What must be the acceleration of the lift for the period of oscillation of the  pendulum to be $T_0/2$ ?