JEE Main · 2024 · 27 Jan 2024 · Shift 1 · Laws of Motion

A train is moving with a speed of

12 m / s

on rails which are 1.5 m apart. To negotiate a curve radius 400 m , the height by which the outer rail should be raised with respect to the inner rail is (Given,

g = 10 m / s^{2}

) :

(A)6.0 cm
(B)5.4 cm✓ Correct
(C)4.8 cm
(D)4.2 cm

Answer: (B)

Solution

For banking with speed

v

, radius

R

tan θ = \frac{v ^{2}}{R g} = \frac{144}{4000} = 0.036

.

For small

θ

tan θ \approx h / L

where

L = 1.5

m is the gauge:

h = L tan θ = 1.5 \times 0.036 = 0.054 m = 5.4 cm

JEE Main · 2024 · 27 Jan 2024 · Shift 1 · Single correct option

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