Question

Choose the correct option according to the angle $\theta$ between force and direction of displacement.

$$\begin{array}{cc}Coloumn1& Coloumn2\\ 1.\theta iszero& i)Workdoneisalwayszero\\ 2.\theta islessthan{90}^0& ii)Workdoneisnon-negative\\ 3.\theta isgreaterthan{90}^0& iii)Workdoneisalwayspositive\\ 4.\theta is{90}^0& iv)Workdoneisneverpositive\end{array}$$

• A. 1-ii, 2-ii, 3-iv, 4-i
• B. 1-iii, 2-ii, 3-iv, 4-i
• C. 1-iii, 2-iii, 3-iv, 4-i
• D. 1-ii, 2-ii, 3-i, 4-iv

Answer 1

The correct option is A

1-ii, 2-ii, 3-iv, 4-i

When the angle is zero, the force$F$ and displacement $d$ are in the same direction. Depending on the value of $F$ and $d$, work may be zero or positive. So work done is non-negative.

When $\theta$ is less than 90°, a component of the force is in the direction of displacement. So work done is non-negative.

When $\theta$ is greater than 90°, a component of force is opposite to the direction of displacement. Therefore the work done can be zero or negative. So work done is never positive.

When $\theta$ is 90°, the force is perpendicular to displacement. So work done is always zero.