A sphere of mass m moving with velocity v collides head-on another sphere of same mass which is at rest. The ratio of final velocity of the second sphere to the initial velocity of the first sphere is ( e is the coefficient of restitution and collision is inelastic)

Question

A sphere of mass m moving with velocity v collides head-on another sphere of same mass which is at rest. The ratio of final velocity of the second sphere to the initial velocity of the first sphere is ( e is the coefficient of restitution and collision is inelastic) (A) (e - 1/2) (B) (e/2) (C) (e + 1/2) (D) e

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-tlgxcriqgm11.png" /> m u + 0 = m u1 + m u2 upsilon1 + upsilon2 = upsilon ....(i) e = ( upsilon2 - upsilon1/ upsilon - 0) e upsilon = upsilon2 - upsilon1 ..(ii) Add equation (i) equation (ii) e upsilon + upsilon = 2 upsilon2 ( upsilon)2 = ( upsilon (. e + 1 .)/2) ( upsilon2/ upsilon) = (e + 1/2)

Q. A sphere of mass $m$ moving with velocity $v$ collides head-on another sphere of same mass which is at rest. The ratio of final velocity of the second sphere to the initial velocity of the first sphere is ( $e$ is the coefficient of restitution and collision is inelastic)

$\frac{e - 1}{2}$

$\frac{e}{2}$

$\frac{e + 1}{2}$

$e$

$m u + 0 = m u_{1} + m u_{2}$
$υ_{1} + υ_{2} = υ$ ....(i)

$e = \frac{υ _{2} - υ _{1}}{υ - 0}$
$e υ = υ_{2} - υ_{1}$ ..(ii)

Add equation (i) & equation (ii)
$e υ + υ = 2 υ_{2}$
$(υ)_{2} = \frac{υ ( e + 1 )}{2}$
$\frac{υ _{2}}{υ} = \frac{e + 1}{2}$

Q. A sphere of mass m moving with velocity v collides head-on another sphere of same mass which is at rest. The ratio of final velocity of the second sphere to the initial velocity of the first sphere is ( e is the coefficient of restitution and collision is inelastic)

2e−1​

2e​

2e+1​

e

mu+0=mu1​+mu2​ υ1​+υ2​=υ ....(i) e=υ−0υ2​−υ1​​ eυ=υ2​−υ1​ ..(ii) Add equation (i) & equation (ii) eυ+υ=2υ2​ (υ)2​=2υ(e+1)​ υυ2​​=2e+1​

Q. A sphere of mass $m$ moving with velocity $v$ collides head-on another sphere of same mass which is at rest. The ratio of final velocity of the second sphere to the initial velocity of the first sphere is ( $e$ is the coefficient of restitution and collision is inelastic)

$\frac{e - 1}{2}$

$\frac{e}{2}$

$\frac{e + 1}{2}$

$e$

$m u + 0 = m u_{1} + m u_{2}$
$υ_{1} + υ_{2} = υ$ ....(i)

$e = \frac{υ _{2} - υ _{1}}{υ - 0}$
$e υ = υ_{2} - υ_{1}$ ..(ii)

Add equation (i) & equation (ii)
$e υ + υ = 2 υ_{2}$
$(υ)_{2} = \frac{υ ( e + 1 )}{2}$
$\frac{υ _{2}}{υ} = \frac{e + 1}{2}$