Work Power Energy

Consider a force $\vec{F}=-x\hat{i}+y\hat{j}$ . The work done by this force in moving a particle from point $A\left(1,0\right)$ to $B\left(0,1\right)$ along the line segment is : (all quantities are in SI units)

A block of mass $m=10\mathrm{kg}$ rests on a horizontal table. The coefficient of friction between the block and the table is$0.05$. When hit by a bullet of mass$50g$ moving with speed $v$, that gets embedded in it, the…

A bob of mass $m$ is suspended by a light string of length $L$. It is imparted a minimum horizontal velocity at the lowest point $A$ such that it just completes half circle reaching the top most position $B$. The ratio…

A car of weight W is on an inclined road that rises by 100 m over a distance of 1km and applies a constant frictional force $\frac{W}{20}$ on the car. While moving uphill on the road at a speed of $10ms^{-1}$ , the car…

Given below is the plot of a potential energy function $U(x)$ for a system, in which a particle is in one dimensional motion, while a conservative force $F(x)$ acts on it. Suppose that $E_{\text{mech}}=8J$, the…

A uniform cable of mass $M$ and length $L$ is placed on a horizontal surface such that its $\left(\frac{1}{n}\right)^{th}$ part is hanging below the edge of the surface. To lift the hanging part of the cable upto the…

The velocity-time graph of a particle of mass $10\mathrm{kg}$ is shown in the figure. The net work done on the particle in the first two seconds of the motion is

A block of mass $1\mathrm{kg}$ is pushed up a surface inclined to horizontal at an angle of $60^{\circ}$ by a force of $10N$ parallel to the inclined surface as shown in figure. When the block is pushed up by $10m$…

For a particle in uniform circular motion, the acceleration $\vec{a}$ at any point $P\left(R,\theta\,\right)$ on the circular path of radius $R$ is (when $\theta\,$ is measured from the positive $x$-axis and $v$ is…

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle $(\theta\,)$ of thread deflection in the extreme position…

A particle is released on a vertical smooth semicircular track from point $X$so that,$OX$makes angle $\theta\,$ from the vertical (see figure). The normal reaction of the track on the particle vanishes at the point $Y$…

A stone tide to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude…