MHT CET · Physics · Laws of Motion

A car is driven on the banked road of radius of curvature 20 m with maximum safe speed. In order to increase its safety speed by \(20 \%\), without changing the angle of banking, the increase in the radius of curvature will be
[Assume friction is same on the road]

A 28.8 m
B \(14 \cdot 4 \mathrm{~m}\)
C 8.8 m
D \(4 \cdot 8 \mathrm{~m}\)

Verified Solution

Answer & Solution

Correct Answer

(C) 8.8 m

Step-by-step Solution

Detailed explanation

\(\frac{v_2}{v_1} = 1 + 0.20 = 1.2\) \(v^2 \propto R\) (as \(\theta\) and \(\mu_s\) are constant)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A car is driven on the banked road of radius of curvature 20 m with maximum safe speed. In order to increase its safety speed by \(20 \%\), without changing the angle of banking, the increase in the radius of curvature will be[Assume friction is same on the road]

Step-by-step Solution

A car is driven on the banked road of radius of curvature 20 m with maximum safe speed. In order to increase its safety speed by \(20 \%\), without changing the angle of banking, the increase in the radius of curvature will be
[Assume friction is same on the road]