Search any question & find its solution
Question:
Answered & Verified by Expert
A body is being raised to a height $h$ from the surface of earth. What is the sign of work done by
(a) applied force and
(b) gravitational force
(a) applied force and
(b) gravitational force
Solution:
2475 Upvotes
Verified Answer
(a) To raise a body upto height $h$, a person will apply the upward force in direction of displacement, angle between the applied force and displacement is $\theta=0^{\circ}$, then
Work done by the applied force is positive,
$$
\begin{aligned}
&\text { Work-done }=\vec{F} \cdot \overrightarrow{d s} \\
&W=F s \cos \theta=F s \cos 0^{\circ}=F s \quad\left(\because \cos 0^{\circ}=1\right) \\
&W=(\text { Positive })
\end{aligned}
$$
(b) Gravitational force acts always in downward direction but displacement in upward direction, so, angle between them is $\theta=180^{\circ}$.
Then work done by the gravitational force
$$
W D=F s \cos 180^{\circ}=-F s\left(\because \cos 180^{\circ}=-1\right)
$$
Hence $W D$ by gravitational force is negative.
Work done by the applied force is positive,
$$
\begin{aligned}
&\text { Work-done }=\vec{F} \cdot \overrightarrow{d s} \\
&W=F s \cos \theta=F s \cos 0^{\circ}=F s \quad\left(\because \cos 0^{\circ}=1\right) \\
&W=(\text { Positive })
\end{aligned}
$$
(b) Gravitational force acts always in downward direction but displacement in upward direction, so, angle between them is $\theta=180^{\circ}$.
Then work done by the gravitational force
$$
W D=F s \cos 180^{\circ}=-F s\left(\because \cos 180^{\circ}=-1\right)
$$
Hence $W D$ by gravitational force is negative.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.