A curved road of 50m radius is banked at correct angle for a given maximum speed vm/s. If the radius of curvature of the road is changed to 200m keeping the same banking angle, the maximum safe speed on the road is
A
2vm/s
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B
0.5vm/s
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C
3vm/s
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D
4vm/s
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Solution
The correct option is A2vm/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=tan−1(v2rg) Condition for banked road is, tanθ=v2rg, therefore, when the radius of curvature of the road is changed to 200m and θ remains the same we have, (v′)2200×gv250×g=1⇒(v′)2=4v2 ∴ The maximum safe speed on the road is v′=2vm/s