$A$ particle of mass $200\,g$ executes a simple harmonic motion. The restoring force is provided by a spring of spring constant $80\,N/m$. The time period is .... $sec$.

$A$ particle of mass $4 M$ which is initially at rest explodes into three pieces of masses $M$,$M$ and $2 M$. The equal masses move along $X$ and $Y$-axes with velocities $4 ~ms^{-1}$ and $6 ~ms^{-1}$,respectively. The magnitude of the velocity of the heavier mass is

$A$ string of length $L$ is fixed at one end and carries a mass $M$ at the other end. The string makes $2/\pi$ revolutions per second around the vertical axis through the fixed end as shown in the figure,then the tension in the string is:

$A$ person standing on a rotating platform has his hands lowered. He suddenly outstretches his arms. The angular momentum

Growth in living organisms occurs by

If $\theta$ is the angle between vectors $\vec{a}$ and $\vec{b}$ and $|\vec{a} \times \vec{b}| = |\vec{a} \cdot \vec{b}|$,then $\theta$ is equal to