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Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is 0.150.15 (g=10 m s−2g = 10 \text{ m s}^{-2}).

1

1.2 m s−21.2 \text{ m s}^{-2}

2

150 m s−2150 \text{ m s}^{-2}

3

1.5 m s−21.5 \text{ m s}^{-2}

4

50 m s−250 \text{ m s}^{-2}

Step-by-Step Solution

For the body to remain stationary on the floor of the car, the pseudo force acting on the body must be balanced by the static frictional force. Thus, ma≤μNma \le \mu N, where N=mgN = mg. Therefore, ma≤μmgma \le \mu mg, which simplifies to a≤μga \le \mu g. Given μ=0.15\mu = 0.15 and g=10 m s−2g = 10 \text{ m s}^{-2}, the maximum acceleration is a=0.15×10=1.5 m s−2a = 0.15 \times 10 = 1.5 \text{ m s}^{-2}.

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