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

$8m{s}^{-2}$

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B

$6m{s}^{-2}$

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C

$4m{s}^{-2}$

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D

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

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Solution

## The correct option is D $2m{s}^{-2}$Step 1. Given dataMass 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, $g=10m{s}^{-2}$] $a=0.2×10$ $a=2m{s}^{-2}$Hence, the correct option is $\left(D\right)$.

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