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 $T_0/2$ ?

Given below are two statements:

Statement $I :$ A second's pendulum has a time period of $1$ second.

Statement $II :$ It takes precisely one second to move between the two extreme positions.

In the light of the above statements, choose the correct answer from the options given below:

Answer the following questions:

$(a)$ Time period of a particle in $SHM$ depends on the force constant $k$ and mass $m$ of the particle:

$T=2 \pi \sqrt{\frac{m}{k}}$. A stmple pendulum executes $SHM$ approximately. Why then is the time pertodof.anondwers period of a pendulum independent of the mass of the pendulum?

$(b)$ The motion of a simple pendulum is approximately stmple harmonte for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that $T$ is greater than $2 \pi \sqrt{\frac{l}{g}} .$ Think of a qualitative argument to appreciate this result.

$(c)$ A man with a wristwatch on his hand falls from the top of a tower. Does the watch give correct time during the free fall?

$(d)$ What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely failing under gravity?

Identify the correct statement 

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