Question

Figure gives the acceleration of a $2.0\text{kg}$ body as it moves from rest along $x-$ axis, while a variable force acts on it from $x=0\text{m}$ to $x=9\text{m}$.
The work done by the force on the body when it reaches $x=4\text{m}$ and $x=7\text{m}$ is

• A. $21\text{J}$ and $33\text{J}$ respectively
• B. $21\text{J}$ and $15\text{J}$ respectively
• C. $42\text{J}$ and $60\text{J}$ respectively
• D. $42\text{J}$ and $30\text{J}$ respectively

Answer 1

The correct option is D $42\text{J}$ and $30\text{J}$ respectively


Here we have acceleration versus displacement graph.
Work done by the force on the body,
when it reaches at $x=4\text{m}$ is
$W_{t=4}$ = Mass of the body $\times$ Area under ABCD
$W_{t=4}=2[(\frac{1}{2}\times 1\times 6)+(3\times 6\left)\right]=42\text{J}$

Work done by the force on the body when it reaches at $x=7\text{m}$ is
$W_{t=7}=W_{t=4}+$ (Mass of the body )(Area under CDE - Area under EFGH)
$=42+2[(\frac{1}{2}\times 1\times 6)-(\frac{1}{2}\times 1\times 6)-(1\times 6\left)\right]$
$W_{t=7}=30\text{J}$