Question

A bomb of mass $6kg$ initially at rest explodes into three identical fragments. One of the fragments moves with a velocity of $10\sqrt{3}\hat{i}$ m/s, another fragment moves with a velocity of $10\hat{j}m/s$, then the third fragment moves with a velocity of magnitude:

• A. $30m/s$
• B. $20m/s$
• C. $15m/s$
• D. $5m/s$

Answer 1

The correct option is B $20m/s$

Since the initial momentum is zero, the final momentum should be zero.
Therefore,

$m\overrightarrow{v_1}+m\overrightarrow{v_2}+m\overrightarrow{v_3}=0$

$\overrightarrow{v_3}=-\overrightarrow{v_1}-\overrightarrow{v_2}$

$\overrightarrow{v_3}=-(10\sqrt{3}\hat{i}+10\hat{j})$

$\mid \overrightarrow{v_3}\mid =\mid -(10\sqrt{3}\hat{i}+10\hat{j})\mid$

$v_3=\sqrt{{\left(10\sqrt{3}\right)}^2+{10}^2}$

$v_3=\sqrt{300+100}=20$ m/s