First slide

The steps in collision

Question

A sphere of mass m moving with a constant velocity u hits another stationary sphere of the same mass' If e is the coefficient of restitution, then ratio of velocities of the two spheres after collision will be

Moderate

A

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

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

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

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

Solution

$e = \frac{V_{2} - V_{1}}{u_{1} - u_{2}} = \frac{V_{2} - V_{1}}{u} or eu = V_{2} - V_{1} Here collision is head on i . e ., u = v_{1} + v_{2} Solving these equations, we get v_{1} = \frac{(1 - e) u}{2} and v_{2} = \frac{(1 + e) u}{2} ∴ \frac{v_{1}}{v_{2}} = \frac{1 - e}{1 + e}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App