A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of the car will be, if the friction coefficient between tyres and road is 0.34. (Take g = 10 m/s2):
Show Hint
For motion on curved roads:
• Use the formula vmax = \(\sqrt{µgr}\) for safe turning.
• Ensure all values are in consistent units for accurate results.
13.4m/s
13m/s
22.4m/s
17m/s
The Correct Option is B
Solution and Explanation
1. Maximum Speed on a Curved Road: - The maximum speed of a vehicle on a curved road is given by:
\[v_\text{max} = \sqrt{\mu gr},\]
where \(\mu\) is the coefficient of friction, g is the acceleration due to gravity, and r is the radius of curvature.
2. Substitute the Values: - \(\mu = 0.34\), g = 10 m/s2, r = 50 m:
\[v_\text{max} = \sqrt{0.34 \times 10 \times 50} = \sqrt{170} \approx 13 \, \text{m/s}.\]
Final Answer: \(\boxed{13 \, \text{m/s}}\)
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