$A$ second's pendulum is mounted in a rocket. Its period of oscillation decreases when the rocket

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

$A$ simple pendulum with length $L$ and mass $m$ of the bob is vibrating with an amplitude $A$. The maximum tension in the string is

$A$ simple pendulum is executing simple harmonic motion with a time period $T$. If the length of the pendulum is increased by $21\%$,the percentage increase in the time period of the pendulum of increased length is ..... $\%$

The time period of a simple pendulum of length $L$ is $T_1$. The time period of a uniform rod of the same length $L$ suspended from one end and oscillating in a vertical plane is $T_2$. The amplitude of oscillation is small in both cases. Then the ratio $\frac{T_1}{T_2}$ is:

The period of a simple pendulum,whose bob is a hollow metallic sphere,is $T$. The period is $T_1$ when the bob is filled with sand,$T_2$ when it is filled with mercury and $T_3$ when it is half filled with mercury. Which of the following is true?