Question

A gardener pushes a lawn roller through a distance $20m$. If he applies a force of $20kg-w$t in a direction inclined at ${60}^o$ to the ground, the work done by him is

• A. 1960 J
• B. 196 J
• C. 1.96 J
• D. 196 KJ

Answer 1

The correct option is A

1960 J

Step1: Given data

A gardener pushes a lawn roller through a distance $S=20m$. If he applies a force of $20kg-w$t in a direction inclined at $\theta ={60}^o$ to the ground.

Step2: Formula used

$W=FS\cos \theta [whereW=workdone,F=cons\tan tforceapplied,S=dispalcement,\theta =anglebetweenFandS]$

Step3: Calculating the work done

Let us write down the given data, force applied by the gardener to push the lawn roller,
$$\begin{gathered} F=20kg-wt \\ \Rightarrow 1kg-wt=9.8N \end{gathered}$$

Therefore,
$$\begin{gathered} F=20kg-wt \\ F=20\times 9.8N \\ F=196N \end{gathered}$$

Displacement of the lawn roller, $S=20m$

The angle between the direction of force applied and direction of displacement is, $\theta ={60}^o$

As the force applied by the gardener is constant, we can use the formula, $W=FS\cos \theta$ to find out the work done by the gardener.
Substituting $F=196N,S=20m,and\theta ={60}^o$ in the formula we get,
$$\begin{gathered} W=196\times 20\times \cos {60}^{\circ } \\ W=196\times 20\times \frac{1}{2}\left[As\cos {60}^{\circ }=\frac{1}{2}\right] \\ \therefore W=1960J \end{gathered}$$

The work done by the gardener in pushing the lawn roller is $1960J$.

Hence, option A is the correct answer.