Question

Force acting on a body varies with time as shown below. If initial momentum of the body is $\vec{p}$, then the time taken by the body to retain its momentum $\vec{p}$ again is

• A. 8 s
• B. $(4+2\sqrt{2})s$
• C. 6 s
• D. Can never obtain

Answer 1

Answer: (B)

$\tan \theta =\frac{1}{2}=\frac{F_0}{t_0-4}$
$\Rightarrow F_0=\frac{t_0-4}{2}$
Total change in momentum should be zero, then only it will retain its initial momentum.
So, positive area of $F-t$ curve should be equal to negative area of $F-t$ curve till time $t_0$.
$\frac{1}{2}(4)(1)=\frac{1}{2}\left(t_0-4\right)F_0$
$8=\frac{\left(t_0-4\right)}{2}\cdot \frac{\left(t_0-4\right)}{2}$
${\left(t_0-4\right)}^2=32$
$t_0=4+2\sqrt{2}$