$(a)$ If the mass of a body is doubled, what happens to its acceleration when acted upon by the same force? Justify your answer.
$(b)$ It is easier to stop a tennis ball than a cricket ball moving with the same speed. Why?
$(c)$ A girl of mass $40 \, kg$ jumps with a horizontal velocity of $5 \, m s^{-1}$ onto a stationary cart with frictionless wheels. The mass of the cart is $10 \, kg$. Find her velocity as the cart starts moving. Assume that there is no external unbalanced force working in the horizontal direction.

(N/A) According to Newton's second law, $F = ma$, which implies $a = F/m$. If the force $F$ remains constant and the mass $m$ is doubled $(2m)$, the new acceleration $a' = F/(2m) = a/2$. Thus, the acceleration becomes half.
$(b)$ Momentum is defined as the product of mass and velocity $(p = mv)$. Since the tennis ball has a smaller mass than the cricket ball, its momentum is lower when moving at the same speed. Therefore, it requires less force to stop it, making it easier to stop.
$(c)$ According to the law of conservation of momentum, since there is no external unbalanced force, the total momentum before the interaction equals the total momentum after the interaction.
Initial momentum = $(m_{girl} \times v_{girl}) + (m_{cart} \times v_{cart}) = (40 \times 5) + (10 \times 0) = 200 \, kg \, m s^{-1}$.
Final momentum = $(m_{girl} + m_{cart}) \times v_{final} = (40 + 10) \times v = 50v$.
Equating the two: $50v = 200$.
$v = 200 / 50 = 4 \, m s^{-1}$.