If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is $\frac{x}{2}$ times its original time period. Then the value of $x$ 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 $\alpha$, is given by

The time period of oscillations of a simple pendulum is $1$ minute. If its length is increased by $44 \%$. then its new time period of oscillation will be ......... $s$

Length of a simple pendulum is $l$ and its maximum angular displacement is $\theta$, then its maximum $K.E.$ is

A simple pendulum with length $100\,cm$ and bob of mass $250\,g$ is executing S.H.M. of amplitude $10\,cm$. The maximum tension in the string is found to be $\frac{x}{40}\,N$. The value of $x$ is $..........$.

Two masses, both equal to $100\, g$, are suspended at the ends of identical light strings of length $\lambda = 1.0\, m$, attached to the same point on the ceiling (see figure). At time $t = 0$, they are simultaneously released from rest, one at angle $\theta_1 = 1^o$, the other at angle $\theta_2 = 2^o$ from the vertical. The masses will collide