Question

A box of mass $2kg$ is placed on the roof of a car. The box would remain stationary until the car attains a maximum acceleration. The coefficient of static friction between the box and the roof of the car is $0.2$ and $g=10m{s}^{-2}$. The maximum acceleration of the car, for the box to remain stationary, is

• A. $8m{s}^{-2}$
• B. $6m{s}^{-2}$
• C. $4m{s}^{-2}$
• D. $2m{s}^{-2}$

Answer 1

The correct option is D

$2m{s}^{-2}$

Step 1. Given data

Mass of the body, $m=2kg$

The coefficient of static friction, $\mu =0.2$

Step 2. Finding the maximum acceleration, $a$

For the box to remain stationary, the applied force, $F$ is equal to the frictional force, $F_r$

$F=F_r$

$ma=\mu mg$ [Where, $g=10m{s}^{-2}$]

$a=0.2\times 10$

$a=2m{s}^{-2}$

Hence, the correct option is $\left(D\right)$.