Question

Define the mechanical advantage of an inclined plane.

• A. M.A = Inclined length/Vertical height
• B. M.A = Effort/Load
• C. M.A = Vertical height/Inclined length
• D. M.A = 1

Answer 1

The correct option is A

M.A = Inclined length/Vertical height

From the above figure, we find that the load (L) have two components which are L cos$\theta$ and L sin$\theta$.
Component L cos$\theta$ is balanced by the reaction force from the inclined plane.

Hence, we need to put effort for the L sin$\theta$ component of the load to balance the block.
So, effort required (E) = L sin$\theta$

Also, Mechanical advantage (MA) = $\frac{\text{Load}}{\text{Effort}}$ = $\frac{\text{L}}{\text{L}sin\theta }$

MA = $\frac{1}{\sin \theta }$ …….(1)

Also, sin $\theta$ = $\frac{\text{perpendicular}}{\text{hypotenuse}}$ = $\frac{h}{l}$ .....(2)

From (1) and (2),
MA = $\frac{1}{\frac{h}{l}}$ = $\frac{l}{h}=\frac{\text{Inclined plane}}{\text{Height}}$