Question

A weightlifter jerks 220kg vertically through $1.5\,m$ and holds still at that height for 2 minutes. The work done by him in lifting and in holding it still are respectively (take $g = 9.8\,m/s$ )
A. $220\,J$, $330\,J$
B. $3234\,J$, $0$
C. $2334\,J$, $10\,J$
D. $0\,J$, $3234\,J$

Answer 1

Hint: We know that work is the product of force and displacement in the direction of force. In the case of lifting, the force is acting upwards and the body is being lifted upwards. Hence force and displacement are in the same direction. So, the angle between them will be zero. Using this we can calculate the value of work. In the second case when the man is holding it in his hands, the displacement will be zero.

Complete step by step answer:
It is given that a weightlifter jerks $220\,kg$ vertically to a height of $1.5\,m$ and holds it still at that height for 2 minutes.
$m = 220\,kg$
$S = 1.5\,m$
$g = 9.8\,m/s$
we need to find the work done by him in lifting it and in holding it still for 2 minutes.
First let us calculate the work done by him in lifting.
We know that work done is the product of force and displacement in direction of force.
In equation form it can be written as
$ W = FS\cos \theta $
Where, F is the force, S is the displacement and $\theta $ is the angle between the direction of force and the direction of displacement.
In the case of lifting we know that the force is acting upwards and the body is moving upwards. So the displacement is in the direction of force.
Hence the angle between the force and displacement is zero.
Here force is equal to the weight.
$F = mg$
$ \Rightarrow F = 220 \times 9.8\,N$
On substituting all the values in the equation, we get
$ \Rightarrow W = 220 \times 9.8 \times 1.5 \times \cos {0^ \circ }$
$ \Rightarrow W = 220 \times 9.8 \times 1.5 \times 1$
$ \Rightarrow W = 3234\,J$
This is the work done in lifting.
Now let us calculate the work done in holding it for 2 minutes.
In this case there is no displacement.
$ \Rightarrow S = 0$
Since work is a product of force and displacement if displacement is zero the work done will also be zero.

Hence the correct answer is option B.

Note:
While calculating the work done remember that the direction of force and displacement is important. Work done is the dot product of force and displacement. Hence, its value depends upon the cosine of the angle made between the force and displacement. When force and displacement are in the same direction work done is said to be positive. When force and displacement are in opposite directions work done is said to be negative.