Question

A shell initially at rest explodes into two pieces of equal mass, then the two pieces will

• A. Be at rest
• B. Move with different velocities in different directions
• C. Move with the same velocity in opposite directions
• D. Move with the same velocity in same direction

Answer 1

The correct option is C

Move with the same velocity in opposite directions

The explanation for the correct option:

(C) Move with the same velocity in opposite directions

The two masses are equal, so to conserve linear momentum which is zero, they should move in opposite directions with equal velocity.

Applying the conservation of momentum, Mass ($m$) and velocity ($v$),

$m_1{v}_1+m_2{v}_2=0$ (because at rest the initial velocity is zero)

Where, $m_1=$mass of the first object

$m_2=$mass of second object

$v_1=$final velocity of the first object

$v_2=$final velocity of the second object

$if{m}_1=m_2=m$

$v_1=-v_2$

negative sign indicates that the second pieces is moving in opposite direction with the first piece.

Therefore they move with the same velocity in opposite directions.

Hence, option (C) is correct.