Question

For a positive value of Force $F$ and displacement $S$, choose the correct relation/s of variation of work done with $\theta$.

• A. Work done is zero when $\theta ={90}^0$.
• B. Work done is positive when $\theta <{90}^0$.
• C. Work done is negative when $\theta >{90}^0$.
• D. Work done is zero when $\theta <{90}^0$.

Answer 1

Answer: (A), (B), (C)

The correct options are
A Work done is zero when $\theta ={90}^0$.
B Work done is positive when $\theta <{90}^0$.
C Work done is negative when $\theta >{90}^0$.

Work done is expressed as
W = F $\times$ S $\times$ cos $\theta$
where
F is the force applied
S is the displacement of the object
$\theta$ is the angle between force and displacement. Depending upon the value of $\theta$ work may be zero, positive or negative.
Case I When $\theta ={90}^0$, the value of $cos\theta =0$. So work done is $0$
Case II When $\theta <{90}^0$, the angle is an acute angle, $cos\theta$ is positive for acute angle. So work done will be positive.
Case III When $\theta$ is greater than 90°, the angle is an obtuse angle $\cos \theta$ is negative for obtuse angle. So work done will be negative.