A sphere of mass m travelling at constant speed v strike another sphere of same mass. If coeff

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5.Work, Energy, Power and Collision

normal

A sphere of mass $m$ travelling at constant speed $v$ strike another sphere of same mass. If coefficient of restitution is $e$, then ratio of velocity of both spheres just after collision is :-

$\frac{1-e}{1+e}$

$\frac{1+e}{1-e}$

$\frac{e+1}{e-1}$

$\frac{e-1}{e+1}$

Solution

$\mathrm{V}_{1}=\frac{\mathrm{m}_{1}-\mathrm{em}_{2}}{\mathrm{m}_{1}+\mathrm{m}_{2}} \mathrm{u}_{1}+\frac{(1+\mathrm{e}) \mathrm{m}_{2}}{\mathrm{m}_{1}+\mathrm{m}_{2}} \mathrm{u}_{2}$

$\mathrm{V}_{2}=\frac{(1+\mathrm{e}) \mathrm{m}_{1}}{\mathrm{m}_{1}+\mathrm{m}_{2}} \mathrm{u}_{1}+\frac{\mathrm{m}_{2}-\mathrm{em}_{1}}{\mathrm{m}_{1}+\mathrm{m}_{2}} \mathrm{u}_{2}$

$\mathrm{m}_{1}=\mathrm{m}_{2}=\mathrm{m}, \quad \mathrm{u}_{2}=0$

$\frac{V_{1}}{V_{2}}=\frac{m-e m}{2 m} u_{1} \times \frac{m+m}{(1+e) m} \frac{1}{u_{1}}$

$\frac{V_{1}}{V_{2}}=\frac{1-e}{1+e}$

Standard 11

Physics

Adjacent figure shows the force-displacement graph of a moving body, what is the work done by this force in displacing body from $x = 0$ to $x = 35\,m$ ? ……….. $\mathrm{J}$

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A ball moving with velocity $2\, m/s$ collides head-on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$, then their velocities (in $m/s$) after collision will be

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Answer carefully, with reasons :

$(a)$ In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact) ?

$(b)$ Is the total linear momentum conserved during the short time of an elastic collision of two balls ?

$(c)$ What are the answers to $(a)$ and $(b)$ for an inelastic collision ?

$(d)$ If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic ?

(Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy).

medium

A body of mass $2\, kg$ slides down a curved track which is quadrant of a circle of radius $1$ metre. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is ………….. $\mathrm{m} / \mathrm{s}$

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Two bodies of masses $0.1\, kg$ and $0.4\, kg$ move towards each other with the velocities $1\, m/s$ and $0.1\, m/s$ respectively. After collision they stick together. In $10\, sec$ the combined mass travels …………… $\mathrm{m}$

normal

A sphere of mass $m$ travelling at constant speed $v$ strike another sphere of same mass. If coefficient of restitution is $e$, then ratio of velocity of both spheres just after collision is :-

Solution

Similar Questions

Adjacent figure shows the force-displacement graph of a moving body, what is the work done by this force in displacing body from $x = 0$ to $x = 35\,m$ ? ……….. $\mathrm{J}$

A ball moving with velocity $2\, m/s$ collides head-on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$, then their velocities (in $m/s$) after collision will be

A body of mass $2\, kg$ slides down a curved track which is quadrant of a circle of radius $1$ metre. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is ………….. $\mathrm{m} / \mathrm{s}$

Two bodies of masses $0.1\, kg$ and $0.4\, kg$ move towards each other with the velocities $1\, m/s$ and $0.1\, m/s$ respectively. After collision they stick together. In $10\, sec$ the combined mass travels …………… $\mathrm{m}$

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