$A$ particle is moving in a circle with uniform speed '$v$'. In moving from a point to another diametrically opposite point:

$A$ particle of mass $m$ moves along a circular path of radius $r$ with a time-dependent centripetal acceleration $a_c = k^2rt^2$,where $k$ is a constant. What is the power delivered to the particle by the force acting on it?

$A$ projectile crosses two walls of equal height $H$ symmetrically as shown. The angle of projection of the projectile is:

Two objects are projected at an angle $\theta^{\circ}$ and $(90-\theta)^{\circ}$ to the horizontal with the same speed. The ratio of their maximum vertical heights is

$A$ projectile is fired from the surface of the earth with a velocity of $5 \, m s^{-1}$ and angle $\theta$ with the horizontal. Another projectile is fired from another planet with a velocity of $3 \, m s^{-1}$ at the same angle and follows a trajectory which is identical to the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in $m s^{-2}$) (Given $g = 9.8 \, m s^{-2}$):

$A$ rod $P$ of length $1 \ m$ is hinged at one end $A$ and there is a ring attached to the other end by a light inextensible thread. Another long rod $Q$ is hinged at $B$ and it passes through the ring. The rod $P$ is rotated about an axis which is perpendicular to the plane in which both the rods are present and the variation between the angles $\theta$ and $\phi$ is plotted as shown. The distance between the hinges $A$ and $B$ is ........ $m$.