$A$ body is moving with constant speed in a circle of radius $10 \ m$. The body completes one revolution in $4 \ s$. At the end of the $3^{rd}$ second,the displacement of the body (in $m$) from its starting point is:

$A$ boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored,the forces acting on the ball at the position $X$ are represented by

$A$ particle of mass $m$ performs uniform circular motion of radius $r$ with linear speed $v$ under the application of force $F$. If $m, v$ and $r$ are all increased by $50 \%$,the necessary change in force required to maintain the particle in uniform circular motion is (in $\%$)

$A$ particle moves in space according to the equation $\vec{r} = (\sin t \hat{i} + \cos t \hat{j} + t \hat{k}) \text{ m}$. Find the time $t$ when the position vector and acceleration vector are perpendicular to each other.

$A$ particle is moving in a circular path. The acceleration and momentum vectors at an instant of time are $\vec{a} = 2 \hat{i} + 3 \hat{j} \ m/s^2$ and $\vec{p} = 6 \hat{i} + 4 \hat{j} \ kg \cdot m/s$. Then the motion of the particle is

If two bodies $A$ and $B$ are projected with the same velocity $u$ but with different angles $\theta_1$ and $\theta_2$ respectively with the horizontal such that both have the same range,then the ratio of the times of flight of the bodies $A$ and $B$ is: