Question

A body moves a distance of $5\text{m}$ along a straight line under the action of a force of $15\text{N}$. If work done by this force is $45\text{J}$, the angle which the force makes with the direction of motion with the horizontal is

• A. ${37}^{\circ }$
• B. ${30}^{\circ }$
• C. ${60}^{\circ }$
• D. ${53}^{\circ }$

Answer 1

The correct option is D ${53}^{\circ }$

Given, distance(displacement) travelled by body along the straight line $=5\text{m}$
Force applied $=15\text{N}$
Work done by force $\left(\text{W}\right)=45\text{J}$

If both force and displacement are along the same direction.
$\therefore$ Workdone $\left(\text{W}\right)=F.s=15\times 5=75\text{J}$
But the given workdone is equal to $45\text{J}$
Therefore, the force is acting on a body by making an angle with direction of motion.
Let the angle be ${}^{\prime }{\theta }^{\prime }$

Then,
Workdone $\left(W\right)=Fs\cos \theta$
$\cos \theta =\frac{W}{Fs}=\frac{45}{15\times 5}=\frac{45}{75}=\frac{3}{5}$
$\therefore \theta ={\cos }^{-1}\left(\frac{3}{5}\right)={53}^{\circ }$

Hence option D is the correct answer