Question

A body of mass 5 m initially at rest explodes in 3 fragments with mass ratio 3:1:1. Two of fragments each of mass 'm' are found to move with a speed of 60 m/s is mutually perpendicular directions. The velocity of third fragment is

• A. $10\sqrt{2}$
• B. $20\sqrt{2}$
• C. $20\sqrt{3}$
• D. $60\sqrt{2}$

Answer 1

Answer: (B)

$20\sqrt{2}$

Given that,

The mass of the body, before collision be $5m$

After the collision, body explodes in 3 fragments.

$m_1=3m$

$m_2=m$

$m_3=m$

Using principle of conservation of linear momentum,

$M\times V=m_1\times v_1+m_2\times v_2$

$3m\times v=\sqrt{(m\times 60{)}^2+(m\times 60{)}^2}$
$=m\times 60\sqrt{2}$
$\Rightarrow v=20\sqrt{2}m/s$

So the velocity of the third fragment is $V=20\sqrt{2}m/s$