$A$ 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 $\left(g=9.8 \ ms^{-2}\right)$

$A$ car of mass $1000 \ kg$ has a motor of efficiency $20 \%$. If burning of one litre of petrol supplies $6 \times 10^7 \ J$ of energy,the amount of petrol used in accelerating the car from rest to $43.2 \ km \ h^{-1}$ is (in $cc$)

$A$ child swings on a swing such that the minimum and maximum heights from the ground are $0.75 \ m$ and $2 \ m$ respectively. The maximum velocity of the swing is ...... $ms^{-1}$.

$A$ ball is falling freely from a height. When it reaches $10 ~m$ height from the ground, its velocity is $v_0$. It collides with the ground, loses $50 \%$ of its energy, and rises back to a height of $10 ~m$. Then the velocity $v_0$ is (in $~m / s$)

Consider two blocks $A$ and $B$ of masses $m_1 = 10 \ kg$ and $m_2 = 5 \ kg$ that are placed on a frictionless table. The block $A$ moves with a constant speed $v = 3 \ m/s$ towards the block $B$ kept at rest. $A$ spring with spring constant $k = 3000 \ N/m$ is attached to the block $B$ as shown in the figure. After the collision,suppose that the blocks $A$ and $B$,along with the spring in a constant compression state,move together. Then the compression in the spring is (neglect the mass of the spring). (in $m$)

$A$ machine with efficiency $2/3$ uses $12 \text{ J}$ of energy to lift a $2 \text{ kg}$ block to a certain height. If the block is allowed to fall freely from that height,what is its velocity when it reaches the ground?