Question

A boy uses a single movable pulley to lift a load of $50\mathrm{kgf}$ to some height. Another boy uses a single fixed pulley to lift the same load to the same height. The ratio of efforts on single movable pulley to efforts on single fixed pulley is,

• A. $2$
• B. $1$
• C. $\frac{1}{2}$
• D. $4$

Answer 1

The correct option is C

$\frac{1}{2}$

Step 1: Find the effort $\left({\mathrm{E}}_1\right)$ of the first boy,

For a single fixed pulley,

$Load\left(\mathrm{L}\right)=50\mathrm{kgf}$
Mechanical advantage $\left(\mathrm{MA}\right)=1$
Since, we know that $\mathrm{MA}=\frac{\mathrm{Load}\left(\mathrm{L}\right)}{\mathrm{Effort}\left(\mathrm{E}\right)}$
Therefore, the effort applied is,

$\begin{array}{rcl}{\mathrm{E}}_1& =& \frac{\mathrm{L}}{\mathrm{MA}}\\ & =& \frac{50\mathrm{kgf}}{1}\\ & =& 50\mathrm{kgf}\end{array}$

Step 2: Find the effort $\left({\mathrm{E}}_2\right)$ of the second boy,

For a single movable pulley,
$Load\left(\mathrm{L}\right)=50\mathrm{kgf}$

Mechanical advantage $(\mathrm{MA}\text{'})=2$

Therefore, the effort applied is,

$\begin{array}{rcl}{\mathrm{E}}_2& =& \frac{\mathrm{L}}{\mathrm{MA}\text{'}}\\ & =& \frac{50\mathrm{kgf}}{2}\\ & =& 25\mathrm{kgf}\end{array}$

Step 3: Calculate the ratio of both the efforts,

The ratio of effort applied is ${\mathrm{E}}_2:{\mathrm{E}}_1$$=50:25$

On simplifying we get the ratio $1:2$

The ratio of efforts applied by them is $\frac{1}{2}$.

Therefore, the correct option is (C).