Question

The $F-x$ graph of a particle of mass $100 \,gm$ is shown in figure. If the particle begins to move from rest at $x=0,$ its velocity at $x=12 m$ is

• A. $10\, ms ^{-1}$
• B. $20\, ms ^{-1}$
• C. $30\, ms ^{-1}$
• D. $40\, ms ^{-1}$

Answer 1

Answer: (D)

Work done by the force = Area under the $F-x$ graph.
From $x=0$ to $12\, m ,$ area under graph
$=\left(\frac{1}{2} \times 4 \times 10\right)+(4 \times 10)+\left(\frac{1}{2} \times 4 \times 10\right)=80 J$
$W=\Delta k$
As particle starts from rest, $W=80 J =\frac{1}{2} m v^{2}-0$
$\frac{1}{2}(0.1\, kg ) v^{2}=80 \,J$
$\Rightarrow v^{2}=\frac{2 \times 80}{0.1}=1600$
or $v=40\, ms ^{-1}$.