First slide

Collisions

Question

A ball moving with speed v hits another identical ball at rest. The two balls stick together after collision. If specific heat of the material of the balls is S, the temperature rise resulting from the collision is

Moderate

A

$\frac{v^{2}}{8 S}$
B

$\frac{v^{2}}{4 S}$
C

$\frac{v^{2}}{2 S}$
D

$\frac{v^{2}}{S}$

Solution

Initial momentum = mv
Final momentum = 2mV
By the conservation of momentum, $mv = 2 mV$
$\Rightarrow V = \frac{v}{2}$
K.E. of the system after the collision = $\frac{1}{2} (2 m) {(\frac{v}{2})}^{2}$
$∴$ loss in K.E. $= \frac{1}{2} {mv}^{2} - \frac{1}{4} {mv}^{2} = \frac{1}{4} {mv}^{2}$
This loss in K.E. will increase the temperature
$∴ 2 m \times s \times Δt = \frac{1}{4} {mv}^{2} \Rightarrow Δt = \frac{v^{2}}{8 s}$

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