Question

A ladder $AB\;$ , $2.5\;m$ long and of weight $150\;N$ has its centre of gravity $1\;m$ from $A\;$ is lying flat on the ground. $A$ weight of $40\;N$ is attached to the end $B\;$ . The work required (in joules) to raise the ladder from the horizontal position to vertical position so that the bottom end $A\;$ is resting in a ditch $1\;m$ below the ground level will be:
(A) $60\;$
(B) $30\;$
(C) $20\;$
(D) $120\;$

Answer 1

To solve this question we will use the concept of work done. We will evaluate the work done to raise the potential energy when the ladder is moved vertically from the horizontal position. After that, we will evaluate the work done to move the attached weight.

Formula used: Work done
$\Rightarrow W = F \times d$
Where $F$ is forced and $d$ is the distance.

Complete step-by-step solution
Here given that the ladder is weighted $150\;N$ with a length of $AB = 2.5\;m$ , and the centre of gravity is given as $1\;m$ away from $A$ lying flat on the ground.
For the first case when the ladder is moved from horizontal to the vertical position, hence moving the ladder weighting of $150\;N$ , since the vertical position of the centre of mass of the ladder is given $1\;m$ from point $A$ as discussed, there will be no change in the potential energy occurs.
Now for the second case when a weight of $40\;N$ is attached at the end of the ladder. As the ladder is now moved to a new position hence the weight of the $40\;N$ which is attached will move about $\Rightarrow \left( {2.5 - 1} \right)m = 1.5\;m$
Hence the weight of $40\;N$ moves $1.5\;m$ above the ground. Therefore the change in potential energy can be given by the work $W$ . Where the formula of work is given as
$\Rightarrow W = F \times d$
Substituting the values of the weight and distance in the formula, hence
$\Rightarrow W = 40\;N \times 1.5\;m$
$\Rightarrow W = 60\;Nm$
$\therefore W = 60\;J$
Hence the work done is given as $60\;J$ .
Therefore the option (A) is the correct answer.

Note
In this question, we have used the formula of work done which can be defined as the force required to displace an object by some distance. It is a scalar quantity. The unit of the work is $N\;m$ or either in joules $J$ .