Embibe Experts Solutions for Chapter: Work, Energy and Power, Exercise 4: Exercise-4

A body is executing simple harmonic motion. At a displacement $x$, its potential energy is $E_1$ and at a displacement $y$, its potential energy is $E_2$. The potential energy $E$ at a displacement $(x+y)$ is

A block of mass $250 \mathrm{g}$ is kept on a vertical spring of spring constant $100 \mathrm{N} {\mathrm{m}}^{-1}$ fixed from below. The spring is now compressed to have a length $10 \mathrm{cm}$ shorter than its natural length and the system is released from this position. How high does the block rise? Take $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}.$

In a projectile motion, $KE$ varies with time as in graph:

The force acting on a body moving along $x$-axis varies with the position of the particle as shown in the figure.

The body is in stable equilibrium at

The graph between kinetic energy $E$ and velocity $v$ is :

A block $\left(B\right)$ is attached to two unstretched springs $S1$ and $S2$ with spring constants $k$ and $4k,$ respectively (see figure I). The other ends are attached to identical supports $M1$ and $M2$ not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block $B$ is displaced towards wall $1$ by a small distance $x$ (figure II) and released. The block returns and moves a maximum distance $y$ towards wall $2.$ Displacements $x$ and $y$ are measured with respect to the equilibrium position of the block $B.$ The ratio $\frac{y}{x}$ is

A toy car of mass $5 \mathrm{kg}$ moves up a rampíunder the influence of force $F$ plotted against displacement $x.$ The maximum height attained is given by

A particle is taken from point $A$ to point $B$ under the influence of a force field. Now it is taken back from $B$ to $A$ and it is observed that the work done in taking the particle from $A$ to $B$ is not equal to the work done in taking it from $B$ to $A.$ If $W_{nc}$ and $W_c$ is the work done by non-conservative forces and conservative forces present in the system respectively, $\Delta U$ is the change in potential energy, $\Delta K$ is the change in kinetic energy, then