Question

Which of the following is not an example of zero work ?
A. The work done by the tension in the string, when a body tied with the string moves along a circular path.
B. When a horse pulls a cart on a level road.
C. The work done by a coolie when he travels on a horizontal platform, with a load on his head.
D. When a person holds some amount of load but does not move from his position.

Answer 1

Hint:To solve this problem learn the definition of work done by a body, Check each option and use the formula for work done to deduce a conclusion from there. Work done by a body is the scalar product of the net applied force and the displacement of the body.

Formula used:
Work done by an object to move a certain displacement is given by,
\[W = \vec F.\vec S\]
where \[W\] is the work done by the object, \[\vec F\] is the net constant applied force and \[\vec S\] is the displacement of the object.

Complete step by step answer:
We know that the work done by an object is the scalar product of the net applied force and the displacement of the body. The mathematical expression is given by, \[W = \vec F.\vec S\] where \[W\] is the work done by the object, \[\vec F\] is the net constant applied force and \[\vec S\] is the displacement of the object. It can be written as, \[W = FS\cos \theta \] where, \[\theta \] is the angle between the force and the displacement.

Now, let’s check the first option:
Option A: We know when a body moves in a circular path the net displacement is zero. So, the work done by the tension in the string, when a body tied with the string moves along a circular path will be zero.
\[W = F \times 0\cos \theta = 0\].

Option B: When a horse pulls a cart on a level road the force applied by the horse is in horizontal direction and the displacement is also in the same direction. So, the angle between the force and the displacement must be zero. So, work done by the horse must be non-zero.
\[W = FS\cos {0^ \circ } = FS\]

Option C: When a coolie moves travels on a horizontal platform, with a load on his head the force acting is the gravitational force but the displacement is along horizontal between the force and the displacement must be perpendicular. So, work done by the horse must be zero.
\[W = FS\cos {90^ \circ } = 0\]

Option D: When a person holds some amount of load but does not move from his position the displacement is always zero as he is at rest. So, the work done by the person due to the gravitational force is zero. Also, force and displacement are perpendicular.
\[W = F \times 0\cos {90^ \circ } = 0\]
Hence, we have in option B that work done by the horse is non-zero.

So, option B is not an example of zero work.

Note: Work done is zero when (i) the force acting on the body is perpendicular to the displacement of the body, (ii) the displacement of the body due to the force is zero then the work done is zero. Remember that though work done by the body is zero but energy loss is not zero by the body.