Question

A $1$ $kg$ stationary bomb is exploded in three parts having mass ratio $1:1:3$. Parts having same mass move in perpendicular directions with velocity $30$ $m/s$, then the velocity of bigger part will be:

• A. $10\sqrt{2}$ $m/s$
• B. $\frac{10}{\sqrt{2}}$ $m/s$
• C. $15\sqrt{2}$ $m/s$
• D. $\frac{15}{\sqrt{2}}$ $m/s$

Answer 1

The correct option is A $10\sqrt{2}$ $m/s$

Two parts having same masses move in perpendicular directions. So, the resultant is the third one having mass $3$ times of the two masses.

So, the resultant is $=\sqrt{(30{)}^2+(30{)}^2}=\sqrt{1800}=30\sqrt{2}$

Since, the bigger part is thrice in mass of the other two parts.

So, $\Rightarrow \frac{30\sqrt{2}}{3}=10\sqrt{2}$ $m{s}^{-1}$

The velocity of bigger part is $10\sqrt{2}$ $m{s}^{-1}$