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?

The angular amplitude of a simple pendulum is $\theta_0$. The maximum tension in its string will be

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle $(\theta)$ of thread deflection in the extreme position will be :

The length of simple pendulum is increased by $44\%$. The percentage increase in its time period will be ….. $\%$

The period of simple pendulum is measured as $T$ in a stationary lift. If the lift moves upwards with an acceleration of $5\, g$, the period will be