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Step-by-Step Solution
Step 1: Understand the Physical Situation
A car is moving on a flat (unbanked) curved road. The maximum safe speed on this curve depends on the frictional force between the tires and the road, which provides the centripetal force to keep the car in circular motion without skidding.
Step 2: Identify the Relevant Formula
The maximum velocity (or minimum velocity required to just avoid skidding at the threshold) is given by:
$v_{\max} = \sqrt{\mu \, r \, g}$
where
$\mu$ is the coefficient of friction,
$r$ is the radius of the circular path,
$g$ is the acceleration due to gravity.
Step 3: Substitute the Given Values
From the question,
$\mu = 0.6$
$r = 150\,\text{m}$
$g = 9.8\,\text{m s}^{-2}$
Hence,
$v_{\max} = \sqrt{0.6 \times 150 \times 9.8}$
Step 4: Calculate the Value
$v_{\max} = \sqrt{0.6 \times 150 \times 9.8}
= \sqrt{0.6 \times 150 \times 9.8}$
Numerically,
$v_{\max} \approx \sqrt{882} \approx 30\,\text{m/s}$
Step 5: Conclude the Answer
The minimum velocity with which the car must traverse the flat curve of radius 150 m to avoid skidding is about $30\,\text{m/s}$. Therefore, the correct answer is 30.
