Question

A force of $15\text{N}$ displaces a box on a horizontal surface through a distance of $10\text{m}$. Calculate the angle which the force makes with the direction of motion of the body, if work done is $75\text{J}$.

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. ${37}^{\circ }$

Answer 1

The correct option is B ${60}^{\circ }$

For calculating the workdone by the force,

Component of fore along sisplacement is $F\cos \theta$


Work done by the force $=\left(F\cos \theta \right)s$
$\Rightarrow F\cos \theta s=75\text{J}$
$\Rightarrow F\times \cos \theta \times 10=75\text{J}$
$\Rightarrow 150\cos \theta =75$ as $(F=15)$
$\Rightarrow \cos \theta =\frac{1}{2}$
$\Rightarrow \theta ={60}^{\circ }$

Hence option B is the correct answer