Question

A smooth sphere of mass M moving with velocity U directly collides elastically with another sphere of mass m at rest. After collision their final velocities are V and v respectively then the value of v is

Answer 1

The answer to the question is $\ \frac{2M}{m+M}\times U$

CALCULATION:

Let the masses of the two spheres are denoted as $m_{1}\ and\ m_{2}\ respectively$

Here, $m_{1} =\ M$  

         $m_{2} =\ m$

Let the initial velocity of the two spheres are denoted as $u_{1}\ and\ u_{2}\ respectively$

Here, $u_{1}=\ U$

         $u_{2} =\ 0$

The two spheres undergo collision. The collision is elastic in nature.

We are asked to calculate the final velocity of the mass m .

Let the final velocities of the two spheres are denoted as $v_{1}\ and\ v_{2}\ respectively$

Here, $v_{1} =\ V$

          $v_{2} =\ v$

The final velocity v is calculated as -

$v_{2}=\ \frac{m_{2}- m_{1}} {m_{1} +m_{2}}\times u_{2} +2\frac{m_{1}} {m_{1} +m_{2}}\times u_{1}$

$v=\frac{m-M}{m+M}\times 0+\ 2\frac{M}{m+M}\times U$

        $=\ \frac{2M}{m+M}\times U$        [ans]

Answer 2

Explanation:

Check the answer here

https://www.studyadda.com/index.php?/question-bank/elastic-and-inelastic-collision/975/69931