If one sphere collides head-on with another sphere of the same mass at rest inelastically. The ratio of their speeds ((v2/v1)) after collision shall be

Question

If one sphere collides head-on with another sphere of the same mass at rest inelastically. The ratio of their speeds ((v2/v1)) after collision shall be (A) ((1 - e)/(1 + e)) (B) (2 e/(1 + e)) (C) ((1 + e)/(1 - e)) (D) e

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-oejks52qm1pp.png" /> v1=((m - e m) u + 0/2 m) v2=(0 + m u (1 + e)/2 m) ∴ (v1/v2)=((1 - e)/(1 + e)) ......... (C) (v2/v1)=((1 + e)/(1 - e))

Q. If one sphere collides head-on with another sphere of the same mass at rest inelastically. The ratio of their speeds $(\frac{v _{2}}{v _{1}})$ after collision shall be

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

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

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

$e$

$v_{1} = \frac{( m - e m ) u + 0}{2 m}$
$v_{2} = \frac{0 + m u ( 1 + e )}{2 m}$
$∴ \frac{v _{1}}{v _{2}} = \frac{( 1 - e )}{( 1 + e )}$ ......... $(C)$
$\frac{v _{2}}{v _{1}} = \frac{( 1 + e )}{( 1 - e )}$

Q. If one sphere collides head-on with another sphere of the same mass at rest inelastically. The ratio of their speeds (v1​v2​​) after collision shall be

(1+e)(1−e)​

(1+e)2e​

(1−e)(1+e)​

e

v1​=2m(m−em)u+0​ v2​=2m0+mu(1+e)​ ∴v2​v1​​=(1+e)(1−e)​ ......... (C) v1​v2​​=(1−e)(1+e)​

Q. If one sphere collides head-on with another sphere of the same mass at rest inelastically. The ratio of their speeds $(\frac{v _{2}}{v _{1}})$ after collision shall be

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

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

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

$e$

$v_{1} = \frac{( m - e m ) u + 0}{2 m}$
$v_{2} = \frac{0 + m u ( 1 + e )}{2 m}$
$∴ \frac{v _{1}}{v _{2}} = \frac{( 1 - e )}{( 1 + e )}$ ......... $(C)$
$\frac{v _{2}}{v _{1}} = \frac{( 1 + e )}{( 1 - e )}$