Question

An elevator is accelerating upwards with an acceleration of $6{\text{m/s}}^2$. Inside it a person of mass $50\text{kg}$ is standing on a weighing machine having rough surface which is kept on an inclined plane having angle of inclination ${60}^{\circ }$. The reading of the weighing machine is -
$($Take $g=10{\text{m/s}}^2)$

• A. $50\text{kg}$
• B. $80\text{kg}$
• C. $40\text{kg}$
• D. $60\text{kg}$

Answer 1

The correct option is C $40\text{kg}$

FBD of man in the elevator frame of reference is shown in the figure.

Here, $ma$ is the pseudo force.

From equilibrium,

$N=(mg+ma)\cos {60}^{\circ }$

$\Rightarrow N=(50\times 10+50\times 6)\times \frac{1}{2}$

$\Rightarrow N=400\text{N}$

$\Rightarrow Mg=400\text{N}$

$\Rightarrow M=40\text{kg}$

Therefore, the reading of the weighing machine is $40\text{kg}$.