Consider an elliptically shaped rail $PQ$ in the vertical plane with $OP = 3 \ m$ and $OQ = 4 \ m$. $A$ block of mass $1 \ kg$ is pulled along the rail from $P$ to $Q$ with a force of $18 \ N$,which is always parallel to the line $PQ$ (see the figure). Assuming no frictional losses,the kinetic energy of the block when it reaches $Q$ is $(n \times 10) \ J$. The value of $n$ is (take acceleration due to gravity $g = 10 \ m/s^2$):

$A$ particle of mass $0.01 \; kg$ travels with velocity given by $4 \hat{i} + 16 \hat{k} \; m s^{-1}$. After some time,its velocity becomes $8 \hat{i} + 20 \hat{j} \; m s^{-1}$. The work done on the particle during this interval of time is ...... $J$.

$A$ 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 $m$ is moving with uniform acceleration such that at time $t_1$ its velocity is $v$. What is the work done on the body at any time $t$?

$A$ body of mass $6 \,kg$ is acted upon by a force which causes a displacement in it given by $x = \frac{t^2}{4} \,m$, where $t$ is the time in seconds. The work done by the force in $2 \,seconds$ is: (in $\,J$)

An object starts sliding on a frictionless inclined plane,and from the same height,another object starts falling freely. Which of the following statements is correct?