Question

A ball of mass $0.5kg$ is moving with a velocity $v$ of $2m/s$. It is subjected to a force of $x$ newton in $2s$. Because of this force, the ball moves with velocity of $3m/s$. 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
$F=ma=m\frac{\Delta v}{\Delta t}$
$\Rightarrow F\Delta t=m\Delta v$
Given, $F=x$ newton,
$\Delta t=2s,v_1=2m/s$
$v_2=3m/s,m=0.5kg$
$\therefore x\times 2=0.5\times 1$
$\Rightarrow x=\frac{0.5}{2}=0.25N$