A bullet of mass $0.02\, kg$ travelling horizontally with velocity $250\, ms^{-1}$ strikes a block of wood of mass $0.23\, kg$ which rests on a rough horizontal surface. After the impact, the block and bullet move together and come to rest after travelling a distance of $40\,m$. The coefficient of sliding friction of the rough surface is $(g = 9.8\, ms^{-2})$
$0.75$
$0.61$
$0.51$
$0.30$
A particle of mass m moving with velocity ${V_0}$ strikes a simple pendulum of mass $m$ and sticks to it. The maximum height attained by the pendulum will be
A body falls towards earth in air. Will its total mechanical energy be conserved during the fall ? Justify.
A ball of mass $10\, kg$ moving with a velocity $10 \sqrt{3} m / s$ along the $x-$axis, hits another ball of mass $20\, kg$ which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along $y-$axis with a speed of $10$ $m / s$. The second piece starts moving at an angle of $30^{\circ}$ with respect to the $x-$axis. The velocity of the ball moving at $30^{\circ}$ with $x-$ axis is $x\, m / s$. The configuration of pieces after collision is shown in the figure below. The value of $x$ to the nearest integer is
A particle of mass $0.1 \,kg$ is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at $x = 0$, its velocity at $x = 12\,m$ is .......... $m/s$
Given in Figures are examples of some potential energy functions in one dimension. The total energy of the particle is indicated by a cross on the ordinate axis. In each case, specify the regions, if any, in which the particle cannot be found for the given energy. Also, indicate the minimum total energy the particle must have in each case. Think of simple physical contexts for which these potential energy shapes are relevant.