Q. 1 kg body explodes into three fragments. The ratio of their masses is 1:1:3. The fragments of same mass move perpendicular to each other with speeds$\ 30{ms}^{- 1}$, while the heavier part remains in the initial direction. The speed of heavier part is
A) $\frac{10}{\sqrt{2}}{ms}^{- 1}$
B) $10\sqrt{2}\ {ms}^{- 1}$
C) $20\sqrt{2}\ {ms}^{- 1}$
D) $30\sqrt{2}\ {ms}^{- 1}$
Explanation
(b) Momentum of third part will be equal to the resultant of momenta of two part
${\ \ \ \ \ \ P}_{3}^{2} = P_{1}^{2} + P_{2}^{2}$
Or $p_{3} = \sqrt{P_{1}^{2} + P_{2}^{2}}$
Or $3mv_{3} = \sqrt{(m \times 30)^{2} + (m \times 30)^{2}}$
Or $v_{3} = \frac{30\sqrt{2}}{3}10\sqrt{2}ms^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.