A mass $m$ slips along the wall of a semispherical surface of radius $R$. The velocity at the bottom of the surface is
$\sqrt {Rg} $
$\sqrt {2Rg} $
$2\sqrt {\pi Rg} $
$\sqrt {\pi Rg} $
A shell of mass $m$ moving with velocity $v$ suddenly breakes into two pieces. The part having mass $\frac{m}{5}$ remains stationary. The velocity of the other part will be
Power supplied to a particle of mass $2\, kg$ varies with time as $P = \frac{{3{t^2}}}{2}$ $watt$ . Here, $t$ is in $seconds$ . If velocity of particle at $t = 0$ is $v = 0$, the velocity of particle at time $t = 2s$ will be ............. $\mathrm{m}/ \mathrm{s}$
A mass $m$ moving horizontally with velocity $v_0$ strikes a pendulum of mass $m$. If the two masses stick together after the collision, then the maximum height reached by the pendulum is
The diagram to the right shows the velocity-time graph for two masses $R$ and $S$ that collided elastically. Which of the following statements is true?
$(I)$ $R$ and $S$ moved in the same direction after the collision.
$(II)$ Kinetic energy of the system $(R$ & $S)$ is minimum at $t = 2$ milli sec.
$(III)$ The mass of $R$ was greater than mass of $S.$
Four particles $A, B, C$ and $D$ of equal mass are placed at four corners of a square. They move with equal uniform speed $v$ towards the intersection of the diagonals. After collision, $A$ comes to rest, $B$ traces its path back with same speed and $C$ and $D$ move with equal speeds. What is the velocity of $C$ after collision