Work Power Energy

A body initially at rest and sliding along a frictionless track from a height $h$ (as shown in the figure) just completes a vertical circle of diameter $AB=D$. The height $h$ is equal to,

A $0.4\mathrm{kg}$ mass takes $8s$ to reach ground when dropped from a certain height $P$above surface of earth. The loss of potential energy in the last second of fall is ______$J$. [Take$g=10ms^{-2}$]

A small particle moves to position $5\hat{i}-2\hat{j}+\hat{k}$ from its initial position $2\hat{i}+3\hat{j}-4\hat{k}$ under the action of force $5\hat{i}+2\hat{j}+7\hat{k}N$. The value of work done will be ______$J$?

An engine is attached to a wagon through a shock absorber of length $1.5m.$The system with a total mass of $40,000\mathrm{kg}$ is moving with a speed of $72\mathrm{km}h^{-1}$ when the brakes are applied to bring it to…

A force $\mathrm{f}=\mathrm{x}^2 \mathrm{y} \hat{\mathrm{i}}+\mathrm{y}^2 \hat{\mathrm{j}}$ acts on a particle in a plane $\mathrm{x}+\mathrm{y}=10$. The work done by this force during a displacement from $(0,0)$ to $(4…

To maintain a speed of $80\mathrm{km}h^{-1}$ by a bus of mass $500\mathrm{kg}$ on a plane rough road for $4\mathrm{km}$ distance, the work done by the engine of the bus will be _____$\mathrm{kJ}$. [The coefficient of…

In the given figure, the block of mass$m$is dropped from the point$'A'$. The expression for kinetic energy of block when it reaches point$'B'$ is

A stone of mass$m$, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is

A person pushes a box on a rough horizontal plateform surface. He applies a force of $200N$over a distance of $15m$. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to…

A particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled$3m$is:

Given below are two statements : Statement I : An object moves from position $r_{1}$ to position $r_{2}$ under a conservative force field $\vec{F}$. The work done by the force is $W=-\int_{r_{1}}^{r_{2}} \vec{F} \cdot…

A block of mass 1 kg , moving along x with speed $\mathrm{v}_{\mathrm{i}}=10 \mathrm{~m} / \mathrm{s}$ enters a rough region ranging from $\mathrm{x}=0.1 \mathrm{~m}$ to $\mathrm{x}=1.9 \mathrm{~m}$. The retarding force…