State whether the following statement is true or false:
Force may or may not produce any motion in a body.

$A$ rocket works on the principle of conservation of

$A$ man throws a ball of mass $0.5\, kg$ vertically upward with a velocity of $25\, m s^{-1}$. Find:
$(a)$ The initial momentum of the ball.
$(b)$ The momentum of the ball at the halfway mark of the maximum height (given $g = 10\, m s^{-2}$).

Why does friction not roll a ball backward if no external force is pushing or pulling it?

Which would require a greater force $-$ accelerating a $1\, kg$ mass at $10\, m s^{-2}$ or a $2\, kg$ mass at $4\, m s^{-2}$?

$(a)$ 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.