The kinetic energy of a particle moving along a circle of radius $R$ depends on the distance $s$ as $K = as^2$,where $a$ is a constant. Then the force acting on the particle is

There are two points $P$ and $Q$ on a projectile path with velocities $v_P$ and $v_Q$ respectively,such that $v_P$ is perpendicular to $v_Q$. If $\alpha$ is the angle that $v_P$ makes with the horizontal at point $P$,find the correct option.

$A$ projectile is fired at an angle of $30^{\circ}$ to the horizontal such that the vertical component of its initial velocity is $80\,m/s$. Its time of flight is $T$. Its velocity at $t=\frac{T}{4}$ has a magnitude of nearly $........\,m/s$.

The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ}$ and $48^{\circ}$ with the horizontal are $R_{1}, R_{2}$ and $H_{1}, H_{2}$ respectively. Choose the correct option:

The centripetal acceleration of a particle in uniform circular motion is $18 \,m/s^2$. If the radius of the circular path is $50 \,cm$, the change in velocity of the particle in a time of $\frac{\pi}{18} \,s$ is (in $\,m/s$)

$A$ particle of mass $1 \ kg$ is projected with an initial velocity $10 \ ms^{-1}$ at an angle of projection $45^{\circ}$ with the horizontal. The average torque acting on the projectile, between the time at which it is projected and the time at which it strikes the ground, about the point of projection in $Nm$ is: