Question

A body at rest explodes into two pieces of unequal mass. The parts will move

• A. Arbitrarily
• B. In the same direction
• C. In opposite direction with equal speeds
• D. In opposite directions with unequal speeds

Answer 1

The correct option is D In opposite directions with unequal speeds

$\because$momentum is conserved

$P_i^{\to }=0P_f^{\to }=m_{f\left(A\right)}{V}_{\left(A\right)}+m_{f\left(B\right)}{V}_{\left(B\right)}=0m_{f\left(A\right)}{V}_{\left(A\right)}^{\to }=-m_{f\left(B\right)}{V}_{\left(B\right)}^{\to }{V}_{\left(A\right)}^{\to }=-\frac{m_{f\left(B\right)}}{m_{f\left(A\right)}}{V}_{\left(B\right)}^{\to }$

both move in opposite directions

$\because m_{f\left(B\right)}\ne m_{f\left(A\right)}{V}_A^{\to }\ne V_B^{\to }$