Question

A body of mass M at rest explodes into three pieces, two of which of mass M/4 each are thrown off in perpendicular directions with velocities of 3 m/s and 4 m/s respectively. The third piece will be thrown off with a velocity of

• A. 1.5 m/s
• B. 2.0 m/s
• C. 2.5 m/s
• D. 3.0 m/s

Answer 1

Answer: (C)

2.5 m/s

Answer 2

Momentum of one piece

$= \frac { M } { 4 } \times 3$

Momentum of the other piece $= \frac { M } { 4 } \times 4$

∴ Resultant momentum

$= \sqrt { \frac { 9 M ^ { 2 } } { 16 } + M ^ { 2 } } = \frac { 5 M } { 4 }$

The third piece should also have the same momentum. Let its velocity be v, then

$\frac { 5 M } { 4 } = \frac { M } { 2 } \times v$ or $v = \frac { 5 } { 2 } = 2.5 \mathrm {~m} / \mathrm { sec }$