A wheel of radius $r$ rolls without slipping with a speed $v$ on a horizontal road. When it is at a point $A$ on the road, a small jump of mud separates from the wheel at its highest point $B$ and drops at point $C$ on the road. The distance $AC$ will be
$v\sqrt {\frac{r}{g}} $
$2v\sqrt {\frac{r}{g}} $
$4v\sqrt {\frac{r}{g}} $
$\sqrt {\frac{{3r}}{g}} $
Two balls of mass $M$ and $2 \,M$ are thrown horizontally with the same initial velocity $v_{0}$ from top of a tall tower and experience a drag force of $-k v(k > 0)$, where $v$ is the instantaneous velocity. then,
A particle reaches its highest point when it has covered exactly one half of its horizontal range. The corresponding point on the displacement time graph is characterised by
A shell is fired at a speed of $200\ m/s$ at an angle of $37^o$ above horizontal from top of a tower $80\ m$ high. At the same instant another shell was fired from a jeep travelling away from the tower at a speed of $10\ m/s$ as shown. The velocity of this shell relative to jeep is $250\ m/s$ at an angle of $53^o$ with horizontal. Find the time (in $sec$) taken by the two shells to come closest.
A body is thrown horizontally from the top of a tower of height $5 \,m$. It touches the ground at a distance of $10 \,m$ from the foot of the tower. The initial velocity of the body is ......... $ms^{-1}$ ($g = 10\, ms^{-2}$)