B M Sharma Solutions for Chapter: Impulse and Collision, Exercise 3: CONCEPT APPLICATION EXERCISE

A heavy ball of mass $2M$ moving with a velocity $v_0$ collides elastically head-on with a cradle of three identical balls each of mass $M$ as shown in figure. Determine the velocity of each ball after collision.

In figure, there are $n$ identical spheres of mass $\mathrm{m}$ suspended with wires of equal length. The spheres are almost in contact with each other. Sphere $1$ is pulled aside and released. If sphere $1$ strikes sphere $2$ with velocity $u$ find an expression for velocity $v_n$ of the $n^{th }$ sphere immediately after being struck by the one adjacent to it. The coefficient of restitution for all the impacts is $e.$

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A mass ${\mathrm{m}}_1$ moves with a great velocity. It strikes another mass ${\mathrm{m}}_2$ at rest in head-on collision. It comes back along its path with low speed after collision. Then find out whether ${\mathrm{m}}_1<{\mathrm{m}}_2$ or ${\mathrm{m}}_1>{\mathrm{m}}_2.$

A ball of mass $4 \mathrm{kg}$ moving with a velocity of $12 \mathrm{m}/\mathrm{s}$ impinges directly on another ball of mass $8 \mathrm{kg}$ moving with velocity of $4 \mathrm{m}/\mathrm{s}$ in the same direction. Find their velocities after impact and calculate the loss of $\mathrm{KE}$ due to impact if $e=0.5.$

Three balls of masses ${\mathrm{m}}_1, {\mathrm{m}}_2$ and ${\mathrm{m}}_3$ are lying in a straight line. The first ball is moved with a certain velocity so that it strikes the second ball directly and itself comes to rest. The second ball collides with the third and is itself reduced to rest. If $e$ is the coefficient of restitution for each ball, write down the relation of ${\mathrm{m}}_3$ in terms of ${\mathrm{m}}_1$ and ${\mathrm{m}}_2.$

Two identical balls $A$ and $B$ lie on a smooth horizontal surface, which gradually merges into a curve to a height $3.2 \mathrm{m}.$ Ball $A$ is given a velocity of $10 \mathrm{m}/\mathrm{s},$ to collide head-on with ball $B,$ which then takes up the curved path. What is the minimum coefficient of restitution, $e,$ for the collision between $A$ and $B$ in order that ball $B$ reaches the highest point $C$ of the curve.

A smooth ball of mass $m$ is suspended from a light string of length $1 \mathrm{m}.$ Another ball of mass $2 \mathrm{m}$ strikes the ball of mass $m$ horizontally with a speed of $u=\sqrt{35} \mathrm{m} {\mathrm{s}}^{-1}.$. The coefficient of restitution for the collision is $e.$ The string becomes loose, when it makes an angle of $30°$ with the horizontal; find the value of $e.$ Use $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

Two balls of masses $\mathrm{m}$ and $2 \mathrm{m}$ and momenta $4p$ and $2p$ collides as shown in figure. During collision, the value of linear impulse between them is $J.$ In terms of $J$ and $p$ find coefficient of restitution ' $e$ '. Under what condition collision is elastic. Also find the condition of perfectly inelastic collision.