Question

A force of 1200 N acts on a 0.5 kg steel ball as a result of a collision lasting 25 ms. If the force is in a direction opposite to the initial velocity of 14 ms$^{-1}$, then the final speed of the steel ball would be?
(a) 24 ms$^{-1}$
(b) 35 ms$^{-1}$
(c) 12 ms$^{-1}$
(d) 46 ms$^{-1}$

Answer 1

Hint: According to the question it is given that in a ball of 0.5kg 1200N force is acted and as result, we see a collision lasting for 25ms. And it is given that if the force is opposite to the initial velocity of 14 ms$^{-1}$ . Then we have to calculate what will be the final speed of the steel ball. To calculate this, we will use the formula and then simply put the given and obtained data, and hence we will get the required result.

Formula Used:
${\rm{F}}\Delta {\rm{t}} = \Delta p$
Whereas F is the force applied.
$\Delta {\rm{t}}$ is the change in time.
$\Delta p$ change in momentum.

Complete step by step solution:
As pe question values of F = 1200 N
t = 25 ms i.e., $\dfrac{{25}}{{1000}}$ and
m = 0.5 kg
v = -14 (negative because in opposite direction)
Also, we know that momentum is nothing but the product of mass and velocity.
Now, substituting accordingly,
$\begin{array}{c}
1200 \times \dfrac{{25}}{{1000}} = 0.5\left[ {v - \left( { - 14} \right)} \right]\\
 \Rightarrow 1.2 \times 50 = v + 14\\
 \Rightarrow v = 60 - 14\\
 \Rightarrow v = 46
\end{array}$
Hence, the final speed of the steel ball is 46 ms$^{-1}$.

Option ‘D’ is correct

Note: A moving object possesses momentum, which is a property determined by its mass and motion and equal to the product of the object's mass and velocity. The rate at which momentum changes is the same as force. Force is defined as mass times acceleration for a constant mass.