BM Sharma Solutions for Chapter: Work, Power, and Energy, Exercise 4: DPP

A particle is moved from $\left(0,0\right)$ to $\left(a,a\right)$ under a force $F=\left(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}\right)$ from two paths. Path $1$ is $OP$ and path $2$ is $OQP$.  Let $W_1$ and $W_2$  be the work done by this force in these two paths. Then,

A spherical ball of mass $20 \mathrm{kg}$ is stationary at the top of a hill of height $100\mathrm{ }\mathrm{m}$. It slides down a smooth surface to the ground, then climbs up another hill of height $30\mathrm{ }\mathrm{m}$ and finally slides down to a horizontal base at a height of $20\mathrm{ }\mathrm{m}$ above the ground. The velocity attained by the ball is

Which of the following graphs is correct between kinetic energy $\left(E\right)$, potential energy $\left(U\right)$ and height $\left(h\right)$from the ground of the particle?

A ball is suspended from the top of a cart by a string of length $1.0\mathrm{ }\mathrm{m}$. The cart and the ball are initially moving to the right at constant speed $V$ as shown in figure $\left(1\right)$. The cart comes to rest after colliding and sticking to a fixed bumper, as in figure $\left(2\right)$. The suspended ball swings through a maximum angle $60°.$ The initial speed $V$ is $($take $g=10 \mathrm{m} {\mathrm{s}}^{-2})$,

The spring block system lies on a smooth horizontal surface. The free end of the spring is being pulled towards right with constant speed $v_0=2\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$. At $t=0 \mathrm{s}$, the spring of constant $k=100 \mathrm{N} {\mathrm{cm}}^{-1}$ is unstretched and the block has a speed $1 \mathrm{m} {\mathrm{s}}^{-1}$ to left. The maximum extension of the spring is,

The potential energy of a particle of mass $m$ free to move along $x$-axis is given by $U=\frac{1}{2}k{x}^2$ for $x<0$and $U=0$for $x\ge 0$($x$ denotes the $x$-coordinate of the particle and $k$ is a positive constant). If the total mechanical energy of the particle is $E$, then its speed at $x=-\sqrt{\frac{2E}{k}}$ is   

In a shot put event, an athlete throws the shot put of mass $10\mathrm{ }\mathrm{kg}$ with an initial speed of $1 \mathrm{m} {\mathrm{s}}^{-1}$ at $45°$ from a height $1.5 \mathrm{m}$ above ground. Assuming air resistance to be negligible and acceleration due to gravity to be $10\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-2}$, the kinetic energy of the shot put when it just reaches the ground will be 

One of the forces acting on a particle is conservative then which of the following statement(s) are true about this conservative force?