Question

A ball of mass $0.5 \,kg$ is moving with a velocity $ v $ of $2 \,m/s$. It is subjected to a force of $ x $ newton in $2\, s$. Because of this force, the ball moves with velocity of $3\, m/s$. The value of $ x $ is

• A. 5 N
• B. 8.25 N
• C. 0.25 N
• D. 1.0 N

Answer 1

Answer: (C)

If a constant force $F$ is applied on a body for a short interval of time $\Delta t$, then the impulse of this force is $F \Delta t$.
When mass of body is $m$, an applying force $F$, for a time interval $\Delta t$, the body suffers a velocity change $\Delta v$, then
$F=m a=m \frac{\Delta v}{\Delta t}$
$ \Rightarrow F \Delta t=m \Delta v$
Given, $F=x$ newton,
$\Delta t=2\, s , v_{1}=2\, m / s$
$ v_{2}=3 \,m / s , m=0.5\, kg$
$\therefore x \times 2=0.5 \times 1 $
$\Rightarrow x=\frac{0.5}{2}=0.25\, N$