$A$ car accelerates from rest to $u \ m/s$. The energy spent in this process is $E \ J$. The energy required to accelerate the car from $u \ m/s$ to $2u \ m/s$ is $nE \ J$. The value of $n$ is ..............

$A$ ball bounces to $80\%$ of its original height. What fraction of its mechanical energy is lost in each bounce?

$A$ lorry and a car moving with the same kinetic energy $(K.E.)$ are brought to rest by applying the same retarding force. Then:

$A$ uniform flexible chain of mass $m$ and length $2l$ hangs in equilibrium over a smooth horizontal pin of negligible diameter. One end of the chain is given a small vertical displacement so that the chain slips over the pin. The speed of the chain when it leaves the pin is

$A$ simple pendulum is released from $A$ as shown in the figure. If $m$ and $l$ represent the mass of the bob and the length of the pendulum respectively,the gain in kinetic energy at $B$ is

$A$ chain of length $L$ and mass $m$ is placed upon a smooth surface as shown. The length of the chain on the incline is $b$. Calculate the velocity of the chain when its end reaches point $B$.