Question

A rod $AB$ of mass $10$$kg$ and length $4$ $m$ rests on a horizontal floor with end $A$ fixed so, as to rotate it in a vertical plane about a perpendicular axis passing through $A$. If the work done on the rod is $100$ $J$, the height to which the end $B$ be raised vertically above the floor is

• A. $1.5m$
• B. $2m$
• C. $1m$
• D. $2.5m$
• E. $3m$

Answer 1

The correct option is B

$2m$

Step 1. Given data:

Mass of the rod $m=10kg$

Length of the rod $L=4m$

Work done on the rod $W=100J$

Acceleration due to gravity $g=10m{s}^{-2}$

Step 2. Find the vertical height of the end $\mathit{B}$ above the floor.

We know the equation to find the work done $W=\frac{mgh}{2}$ (where $h$ is the vertical height)

$\Rightarrow h=\frac{2W}{mg}$

By substituting the given data we get

$$\begin{gathered} \Rightarrow h=\frac{2\times 100}{10\times 10} \\ \Rightarrow h=2m \end{gathered}$$

Thus the vertical height of the end $B$ from the floor is $2m$

Hence, the option $\text{'}B\text{'}$ is correct.