Two bodies are thrown up at angles of $45^\circ$ and $60^\circ$,respectively,with the horizontal. If both bodies attain the same vertical height,then the ratio of the velocities with which these are thrown is:

$A$ body is revolving with a constant speed along a circle. If its direction of motion is reversed but the speed remains the same,then which of the following statements is true?

$A$ particle of mass $m$ is executing uniform circular motion on a path of radius $r$. If $p$ is the magnitude of its linear momentum,then the radial force acting on the particle is:

At a given instant of time,the position vector of a particle moving in a circle with a velocity $\vec{v} = 3 \hat{i} - 4 \hat{j} + 5 \hat{k}$ is $\vec{r} = \hat{i} + 9 \hat{j} - 8 \hat{k}$. Its angular velocity $\vec{\omega}$ at that time is:

The range of a projectile is $100 \ m$. Its kinetic energy will be maximum after covering a horizontal distance of: (in $m$)

$A$ ball is released from rest from point $P$ of a smooth semi-spherical vessel as shown in the figure. The ratio of the centripetal force and normal reaction on the ball at point $Q$ is $A$,while the angular position of point $Q$ is $\alpha$ with respect to point $P$. Which of the following graphs represents the correct relation between $A$ and $\alpha$ when the ball goes from $Q$ to $R$?