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Question

A curved road of 50 m radius is banked at correct angle for a given maximum speed v m/s. If the radius of curvature of the road is changed to 200 m keeping the same banking angle, the maximum safe speed on the road is

A
2v m/s
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B
0.5v m/s
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C
3v m/s
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D
4v m/s
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Solution

The correct option is A 2v m/s

By the free body diagram and writing the force equation we get,

Ncosθ=mg ...(i)
Nsinθ=mv2r ...(ii)
Now by dividing both the above equations, we get,

θ=tan1(v2rg)
Condition for banked road is,
tanθ=v2rg, therefore, when the radius of curvature of the road is changed to 200 m and θ remains the same we have,
(v)2200×gv250×g=1 (v)2=4v2
The maximum safe speed on the road is
v=2v m/s

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