$A$ uniform chain of length $3\, m$ and mass $3\, kg$ overhangs a smooth table with $2\, m$ laying on the table. If $k$ is the kinetic energy of the chain in joules as it completely slips off the table,then the value of $k$ is (Take $g = 10\, m/s^2$).

$A$ cricket ball of mass $0.15 \, kg$ is thrown vertically up by a bowling machine so that it rises to a maximum height of $20 \, m$ after leaving the machine. If the part pushing the ball applies a constant force $F$ on the ball and moves a distance of $0.2 \, m$ while launching the ball,the value of $F$ (in $N$) is $(g = 10 \, m/s^2)$.

$A$ body of mass $m$ dropped from a height $h$ reaches the ground with a speed of $0.8 \sqrt{gh}$. The value of work done by the air friction is $.....$

State the principle of conservation of mechanical energy for a conservative force.

An object of mass $8 \ kg$ moves under the influence of a force. The position of the object varies with time as $x = \frac{1}{2} t^2$,where $x$ is in meters and $t$ is in seconds. Find the work done by the force in the first $2 \ s$ in $J$.

$A$ block of mass $m$ is suspended vertically from an elastic string with a force constant $k = mg/a$. Initially,the string is at its natural length and the block is allowed to fall freely. What will be its kinetic energy when the block passes through the equilibrium position?