Question

A particle of mass 0.1 kg is subjected to a force which varies with distance as shown in the figure. If it starts its journey from rest at x = 0, its velocity at x = 12 m is

• A. Zero
• B. $20\sqrt{2}m/s$
• C. $20\sqrt{3}m/s$
• D. $40m/s$

Answer 1

The correct option is D

$40m/s$

Work done = Area under the F-x graph
$=\frac{1}{2}\times 10\times 4+10\times 4+\frac{1}{2}\times 10\times 4=80J$
Now, work done = increase in kinetic energy. If v is the velocity at x = 12 m, then increase in K.E. $=\frac{1}{2}m{v}^2$.
$\therefore \frac{1}{2}m{v}^2=80$
$\Rightarrow v^2=\frac{80\times 2}{m}=\frac{80\times 2}{0.1}=1600$
$\Rightarrow v=40m{s}^{-1}$
Hence, the correct choice is (d).