The relationship between force and position is shown in the figure given (in one-dimensional case). The work done by the force in displacing a body from $x = 1 \, cm$ to $x = 5 \, cm$ is .......... $ergs$.

$A$ toy car of mass $5 \, kg$ moves up a ramp under the influence of a force $F$ plotted against displacement $x$ as shown in the graph. The maximum height attained is given by:

$A$ force of $(5+3x) \text{ N}$ acts on a body of mass $20 \text{ kg}$ along the $x$-axis and displaces it from $x = 2 \text{ m}$ to $x = 6 \text{ m}$. The work done by the force is $.... \text{ J}$.

$A$ force $F = 20 + 10y$ acts on a particle in the $y$ direction,where $F$ is in newton $(N)$ and $y$ is in meter $(m)$. The work done by this force to move the particle from $y = 0$ to $y = 1 \; m$ is ...... $J$.

For a particle moving under the action of a variable force,the kinetic energy-position $(K-x)$ graph is given. Then:

$A$ particle of mass $10\,g$ moves in a straight line with retardation $2x$,where $x$ is the displacement in $SI$ units. Its loss of kinetic energy for the above displacement is $\left(\frac{10}{x}\right)^{-n}\,J$. The value of $n$ will be $............$.