Question

If a cabin is descending vertically with acceleration $a$ and action by mass $M$ on the floor of the cabin is $\frac{9Mg}{10}$ then $a$ equal to:

• A. $g$
• B. $\frac{g}{10}$
• C. $\frac{9}{10}g$
• D. $\frac{10}{9}g$

Answer 1

The correct option is B

$\frac{g}{10}$

Step 1: Given

Acceleration $=a$

Mass$=M$

Reaction force, $R=\frac{9Mg}{10}$

Step 2: Determine the acceleration,

The diagrammatic representation of the given case is,

The weight of the body is acting downwards.

The acceleration of the lift is acting upwards.

The reaction force is in the opposite direction of the motion.

From the free body diagram,

$$\begin{gathered} R+Ma=Mg \\ a=\frac{Mg-R}{M} \\ =\frac{Mg-{\displaystyle \frac{9Mg}{10}}}{M} \\ =g-\frac{9}{10}g \\ =\frac{g}{10} \end{gathered}$$

Hence, option (B) is the correct option.