$A$ particle is performing uniform circular motion with angular momentum $L$. If the frequency of motion is doubled and the kinetic energy is halved,the new angular momentum will be

$A$ particle of mass $m$ moves with constant speed $v$ on a circular path of radius $r$ as shown in the figure. The average force on it during its motion from $A$ to $B$ is

Range of a bullet fired at $45^o$ to the horizontal is $980 \, m$. If the bullet is fired at the same angle from a car travelling horizontally at $18 \, km/h$ towards the target,then the range will be increased by:

$A$ projectile is thrown with velocity $v$ making an angle $\theta$ with the vertical. It reaches a maximum height $H$. The time of flight is:

Two particles having mass $M$ and $m$ are moving in a circular path having radius $R$ and $r$. If their time periods are the same,then the ratio of their angular velocities will be:

One end of a rod of length $L=1 \,m$ is fixed to a point on the circumference of a wheel of radius $R=1 / \sqrt{3} \,m$. The other end is sliding freely along a straight channel passing through the centre $O$ of the wheel as shown in the figure. The wheel is rotating with a constant angular velocity $\omega$ about $O$. The speed of the sliding end $P$,when $\theta=60^{\circ}$ is