Question

Momentum is the ability of imparting or tending to impart motion to other bodies. The total momentum of a system remains conserved if no external force is acting it. This is calculated by the formula, $\vec{p}=m\vec{v}$. Consider a situation where a cart carrying five boys is moving without friction due to inertia along a straight horizontal road, with a speed of $10m/s$. After travelling certain distance, a boy jumps from the cart with a speed of $2m/s$ with respect to the cart in opposite direction to it. Then, second boy jumps with the same speed w.r.t. the cart, but in a perpendicular direction to the cart. The mass of the cart is $100kg$ and mass of each boy is $20kg$.
Which of the following statement is true?

• A. Linear momentum can't be conserved as boys are jumping out.
• B. Even after jumping, momentum of the system is conserved.
• C. Momentum is conserved between the jumping of first and second boy.
• D. Momentum is said to be conserved as no external force is acting.

Answer 1

Answer: (B)

$\sum {\vec{F}}_{\text{sys}}^{\text{ ext}}=0$
$\Rightarrow {\vec{p}}_{\text{sys }}=$ constant