$A$ pendulum suspended from the ceiling of a train has a period $T$ when the train is at rest. When the train travels the same distance per unit time,the period of oscillation is

In an engine,the piston undergoes vertical simple harmonic motion with an amplitude of $7\, cm$. $A$ washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston is close to ...... $Hz$.

$A$ simple pendulum of period $T$ has a metal bob which is negatively charged. If it is allowed to oscillate above a positively charged metal plate,its period will

$A$ simple pendulum,suspended from the ceiling of a lift,has a period of oscillation $T$,when the lift is at rest. If the lift starts moving upwards with an acceleration $a = 3g$,then the new period will be

The metallic bob of a simple pendulum has the relative density $\rho$. The time period of this pendulum is $T$. If the metallic bob is immersed in water,then the new time period is given by

$A$ light balloon filled with helium of density $\rho_{He}$ is tied to a light string of length $L.$ The string is tied to the ground forming an "inverted" simple pendulum (figure). If the balloon is displaced slightly from equilibrium as in figure and released, the period of the motion is. Take the density of air to be $\rho_{air}$. Assume the air applies a buoyant force on the balloon but does not otherwise affect its motion.