Question 40: 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 0.15\left(\mathrm{~g}=10 \mathrm{~m} \mathrm{~s}^{-2}\right).
(1) 1.5 \mathrm{~m} \mathrm{~s}^{-2}
(2) 50 \mathrm{~m} \mathrm{~s}^{-2}
(3) 1.2 \mathrm{~m} \mathrm{~s}^{-2}
(4) 150 \mathrm{~m} \mathrm{~s}^{-2}
Answer: Option (1)
Explanation:
For the body to remain stationary with respect to the car, the frictional force must provide the necessary acceleration.
The maximum static friction force is given by f_{\max}=\mu_s N.
Here, the normal reaction is N=mg.
Thus, the maximum frictional force is f_{\max}=\mu_s mg.
This frictional force provides the maximum possible acceleration a_{\max} to the body, so
f_{\max}=ma_{\max}.
Therefore, ma_{\max}=\mu_s mg.
Canceling m from both sides, we get
a_{\max}=\mu_s g.
Substituting the given values,
a_{\max}=0.15 \times 10.
Hence, a_{\max}=1.5 \mathrm{~m\,s^{-2}}.
Therefore, the correct answer is Option (1).