Embibe Experts Solutions for Chapter: Work, Energy and Power, Exercise 3: Level 3

A particle with total mechanical energy which is small and negative is under the influence of a one dimensional potential $U\left(x\right)=\frac{x^4}{4}-\frac{x^2}{2} \mathrm{J}$, where $x$ is in meters. At time $t=0 \mathrm{s},$ it is at $x=-0.5 \mathrm{m}.$ Then at a later time it can be found,

The blocks $A$ and $B$ shown in the figure have masses, $M_{\mathrm{A}}=5 \mathrm{kg}$ and $M_{\mathrm{B}}=4 \mathrm{kg}$. The system is released from rest. The speed of $B$ after $A$ travels a distance $1 \mathrm{m}$ along the incline is,

Block $A$ of mass $m$ is placed on a plank $B$. A light support $S$ is fixed on plank $B$ and is attached with the block $A$ with a spring of spring constant $K$. Consider that initially spring is in its natural length. Find the maximum compression in the spring, if the plank $B$ is given an acceleration $a$. All the surfaces are smooth 

The potential energy of a $0.64 \mathrm{kg}$ particle moving along the $x$ -axis is given by $U\left(x\right)=8{\mathrm{x}}^2$, where, $U$ is in joules and $x$ is in meters. When the particle is at $x=1.0 \mathrm{m}$, it is travelling in the positive $x$ -direction with a speed $5.0 \mathrm{m} {\mathrm{s}}^{-1}$. It stops momentarily to turn around at $x$, where $x$

A body of mass $m$ dropped from a certain height strikes a light vertical fixed spring of stiffness $k\mathit{.}$ The height of its fall before touching the spring if the maximum compression of the spring is equal to $\frac{3mg}{k}$ is:

A string of negligible mass going over a clamped pulley of mass $\mathrm{m}$ supports a block of mass $M$ as shown in the figure. The force on the pulley by the clamp is given by

Two objects are initially at rest on a frictionless surface. Object $1$ has greater mass than object $2$. Some constant force starts to act on each object. The force is removed from each object after it accelerates over a distance $d$. After the force is removed from both objects, which of the statements is correct ($p:$ momentum;$K:$ kinetic energy)?

A heavy elevator is moving upwards with constant velocity $5 \mathrm{m} {\mathrm{s}}^{-1}$. At time $t=0$, a ball situated at a distance of $100 \mathrm{m}$ from the elevator is dropped. Find the velocity of the ball just after the collision(elastic) $($use $\left.g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$.