A ball will a speed of $9\, m / s$ collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of $30^{\circ}$ with the original direction. The ratio of velocities of the balls after collision is $x : y$ where $x$ is........
$3$
$2$
$0$
$1$
A $6 \,kg$ bomb at rest explodes into three equal pieces $P, Q$ and $R$. If $P$ flies with speed $30 \,m / s$ and $Q$ with speed $40 \,m / s$ making an angle $90^{\circ}$ with the direction of $P$. The angle between the direction of motion of $P$ and $R$ is about
A $^{238}U$ nucleus decays by emitting an $\alpha$ particle of speed $v\,m{s^{ - 1}}$. The recoil velocity of the residual nucleus is (in $m{s^{ - 1}}$)
A $1 \;kg$ stationary bomb is exploded in three parts having mass $1: 1: 3$ respectively. Parts having same mass move in perpendicular direction with velocity $30\; ms ^{-1}$, then the velocity of bigger part will be
A bullet $10\,g$ leaves the barrel of gun with a velocity of $600\,m / s$. If the barrel of gun is $50\,cm$ long and mass of gun is $3\,kg$, then value of impulse supplied to the gun will be $.....\,Ns$
A spring is compressed between two toy carts of mass $m_1$ and $m_2$. When the toy carts are released, the springs exert equal and opposite average forces for the same time on each toy cart. If $v_1$ and $v_2$ are the velocities of the toy carts and there is no friction between the toy carts and the ground, then :