The path length of oscillation of a simple pendulum of length $1 \,m$ is $16 \,cm$. Its maximum velocity is (Take $g = \pi^2 \,m/s^2$).

The length of a simple pendulum is increased by $2\%$. Its time period will

$A$ positively charged pendulum is oscillating in a uniform electric field pointing upwards. How does its time period compare to the time period when it oscillates without an electric field?

$A$ simple pendulum of length $1 \ m$ and having a bob of mass $100 \ g$ is suspended in a car, moving on a circular track of radius $100 \ m$ with uniform speed $10 \ m/s$. If the pendulum makes small oscillations in a radial direction about its equilibrium position, then its time period is given by $T = 2\pi / \alpha^{1/4}$. The value of $\alpha$ is (Take $g = 10 \ m/s^2$)

$A$ man with a wrist watch and a pendulum clock rises to the top of a $TV$ tower. Both the wrist watch and the pendulum clock accidentally fall from the top of the tower. Then:

$A$ small sphere oscillates simple harmonically in a watch glass whose radius of curvature is $1.6 \text{ m}$. The period of oscillation of the sphere is (Acceleration due to gravity $g = 10 \text{ m/s}^2$)