Question

Choose the correct option according to the angle 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 value of $\cos \theta$ is one and then depending on the value of F and d, work may be zero or positive. So work done is non-negative. Same is the case when $\theta$ is less than 90°. When $\theta$ is greater than 90° then value of $\cos \theta$ is negative. So work done is never positive. However, it can be zero depending on force and the displacement value. When $\cos \theta$ is 90°, then value of $\cos \theta$ is zero. So work done is always zero.