Question

Sneha has to lift a load of mass 50 kg to a height 1 m. She can exert a maximum effort of 250 N, so she uses an inclined plane to lift the load up. What should be the minimum length of the plank used by her? (take g = 10 N/kg)

• A. 2 m
• B. 1 m
• C. 2.5 m
• D. 1.5 m

Answer 1

The correct option is A

2 m

Given, maximum effort (E) = 250 N
Load (L) = mg = 50 x 10 = 500 N
Height (AC) = 1 m

Let angle made by inclined plane with the horizontal be $\theta$.

From the figure above,

E = L sin $\theta$
$\Rightarrow$ 250 = 500 sin $\theta$

sin $\theta$ = $\frac{250}{500}$ = $\frac{1}{2}$ ...(i)

Also, from triangle ABC,
sin $\theta$ = $\frac{\text{height}}{\text{length of the plane}}$ = $\frac{\text{AC}}{\text{AB}}$ ........(ii)

From equation (i) and (ii), we get

$\frac{\text{AC}}{\text{AB}}$ = $\frac{1}{2}$

$\Rightarrow \frac{1}{\text{AB}}$ = $\frac{1}{2}$

$\Rightarrow$ AB = 2 m