Question

A shell initially at rest explodes into two equal fragments A and B. Then :

• A. A and B have collinear velocities in the same direction
• B. A and B have equal speeds but opposite velocities
• C. A and B have equal speeds but their velocities inclined to each other
• D. A and B may have unequal speeds but opposite velocities.

Answer 1

The correct option is B A and B have equal speeds but opposite velocities

Since shell is initially at rest, it means initially the momentum is zero.
So after the explosion, the resultant momentum of its fragments A & B must also be equal to zero.
Let the mass of fragments be $m_1\&m_2$ and since the fragments A & B are equal therefore, $m_1=m_2$
Hence the conservation of linear momentum:
$m_1{v}_1+m_2{v}_2=0\Rightarrow m_1{v}_1+m_1{v}_2=0\Rightarrow v_1={-v}_2$
Therefore, A and B have equal speeds but opposite velocities.