Question

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

$\begin{array}{cc}\text{Coloumn 1}& \text{Coloumn 2}\\ 1.\theta \text{is zero}& \text{i) Work done is always zero}\\ 2.\theta \text{is less than}{90}^0& \text{ii) Work done is non-negative}\\ 3.\theta \text{is greater than}{90}^0& \text{iii) Work done is always positive}\\ 4.\theta \text{is}{90}^0& \text{iv) Work done is never positive}\end{array}$

• 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.