$A$ force $\overrightarrow{F} = 4 \hat{i} - 15 \hat{j} \text{ N}$ acts on a body, resulting in a displacement of $\overrightarrow{S} = 6 \hat{i} \text{ m}$. If the body had a kinetic energy of $7 \text{ J}$ at the beginning of the displacement, what is the kinetic energy at the end of the displacement (in $\text{ J}$)?

$A$ body of mass $2\, kg$ is thrown up vertically with a kinetic energy of $490\, J$. If the acceleration due to gravity is $9.8\, m/s^2$,then the height at which the kinetic energy of the body becomes half its original value is ............ $m$.

$A$ uniform flexible chain of mass $m$ and length $2l$ hangs in equilibrium over a smooth horizontal pin of negligible diameter. What will be the speed of the chain when it leaves the pin?

$A$ demonstration apparatus on a table in the lab is shown in the diagram. It consists of a metal track (shown as a thick solid line in the figure) along which a perfectly spherical marble can roll without slipping. In one run,the marble is released from rest at a height $h$ above the table on the left section,rolls down one side and then up the other side without slipping,briefly stopping when it has reached $h_1$. Assuming the table to be horizontal and neglecting air drag as well as any energy loss due to rolling,which of the following is true?

$A$ 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 $.....$

For a body of mass $1 \ kg$,the $U-x$ graph is shown in the figure. If the body is released from rest at $x = 2 \ m$,then its speed when it crosses $x = 5 \ m$ is: