If $250 \,J$ of work is done in sliding a $5 \,kg$ block up an inclined plane of height $4 \,m$. value of Work done against friction is ............. $J$ $\left(g=10 \,ms ^{-2}\right)$

$A$ particle with constant total energy $E$ moves in one dimension in a region where the potential energy is $U(x)$. The speed of the particle is zero where

A particle gets displaced by $\Delta \,\vec r = \,(2\hat i + 3\hat j + 4\hat k)$ $m$ under the action of a force $\vec F = \,(7\hat i + 4\hat j + 3\hat k)$ The change in its kinetic energy is ............... $\mathrm{J}$

The graph between the resistive force $ F$ acting on a body and the distance covered by the body is shown in the figure. The mass of the body is $25\, kg$ and initial velocity is $2\, m/s$. When the distance covered by the body is $4m$, its kinetic energy would be .............. $\mathrm{J}$

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

A number of identical cubical blocks of edge $'a'$ and mass $m$ are lying on a horizontal table. The work done on the blocks in arranging them in a column of height $(n + 1)a$ on the table is