$A$ 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 $g = 10 \text{ m/s}^2$)

$A$ pendulum clock is running slow. To correct its time,we should

$A$ block of mass $m$ is sliding on a fixed frictionless concave surface of radius $R$. It is released from rest at point $P$ which is at a height of $H \ll R$ from the lowest point $Q$.
$(a)$ What is the potential energy as a function of $\theta$,taking the lowest point $Q$ as the reference level for potential energy?
$(b)$ What is the kinetic energy as a function of $\theta$?
$(c)$ What is the time taken for the particle to reach from point $P$ to the lowest point $Q$?
$(d)$ How much force is exerted by the block on the concave surface at the point $Q$?

The velocity of a simple pendulum is maximum at

$A$ child is sitting on a swing which performs $S.H.M$. It has minimum and maximum heights from the ground of $0.75 \,m$ and $2 \,m$ respectively. Its maximum speed will be $\left[g=10 \,m/s^2\right]$

The time period of a simple pendulum is $4 \ s$ at a place on the Earth where the acceleration due to gravity is $\pi^2 \ ms^{-2}$. The length of the pendulum in meters is: