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\[\begin{align}

& A)F=1N,S=1m,\theta =0{}^\circ \\

& B)F=1N,S=1m,\theta =90{}^\circ \\

& C)F=0.1N,S=1m,\theta =0{}^\circ \\

& D)F=0.1N,S=10m,\theta =90{}^\circ \\

\end{align}\]

Answer

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Work done by a body is calculated as the dot product of force applied to do the work and distance moved by the object. We must know that even there is application of a force, work done by a body can be positive, negative or zero.

\[W=F\cdot d=\left| F\cos \theta \right|\times \left| d \right|\]

Work done by a body is defined as the product of distance moved by the object in the direction of force applied on it. Work is energy and its S.I. unit is joule.

We will use the formula \[W=\left| F\cos \theta \right|\times \left| d \right|\]to determine the work done by each case as per given in the question. Where, \[F\] is the force applied on the body and \[d\] is the distance moved.

We can easily avoid checking if the work done by second and fourth cases is \[1J\] because the angle between the force applied and distance moved by the object in each case is given as \[90{}^\circ \]. But we know \[\cos \left( 90{}^\circ \right)=0\]. So, the work done in second and fourth cases is zero.

Now, if we consider the first case, we have \[F=1N,S=1m,\theta =0{}^\circ \]. So, the work done in this case will be

\[W=\left| F\cos \theta \right|\times \left| d \right|=1\times \cos \left( 0 \right)\times 1=1J\]

So the work done in the first case is \[1J\].

Now, if we take the third case, work done will be,

\[W=\left| F\cos \theta \right|\times \left| d \right|=0.1\times \cos \left( 0 \right)\times 1=0.1J\]

So the work done in the third case is \[0.1J\].

We got the work done in the first case as \[1J\]. So, the correct answer is option A.

We can solve this question quickly by eliminating the option in which the angle between force applied and distance travelled is given as \[90{}^\circ \]. Work done one a body could be positive, zero or negative. This anomaly arises because, if the force applied and the distance moved by the objects are in the same direction, then it will be positive. If they are in the opposite direction, work done will be negative. Now, work done will be zero if the angle between applied force and distance is \[90{}^\circ \].