Question

A shell of mass $100\, g$ moving with speed of $50\, m\, s ^{-1}$ along a straight line inclined at an angle $\tan ^{-1}\left(\frac{4}{3}\right)$ to the horizontal bursts into two pieces. The piece of mass $60\, g$ starts moving horizontally with a speed of $50 \,m\, s ^{-1}$. The other piece moves with a speed of

• A. $50\, m\, s ^{-1}$ opposite to the first piece
• B. $100\, m\, s ^{-1}$ in vertically downward direction
• C. $50\, m\, s ^{-1}$ in the same direction as the first piece
• D. zero (remains at rest)

Answer 1

Answer: (B)

Initial momentum
$=\frac{100}{1000} \times 50 kg m s ^{-1}=5 \,kg\, m\, s ^{-1}$
Horizontal momentum $=3\, kg\, m\, s ^{-1}$
Vertical momentum $=4\, kg\, m\, s ^{-1}$
The velocity of other piece of mass $40\, g$
$=\frac{4 \,kg\, m\, s ^{-1}}{0.04\, kg }=100\, m \,s ^{-1}$

To conserve momentum, it should be directed vertically downward