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Banked curve: banking height or maximum safe speed

This type of question, asked 2 times: 27 Jan 2024, 6 Apr 2024. All 2 questions below, oldest first.

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  1. Question 1

    27 Jan 2024

    6
    A train is moving with a speed of 12 m/s12\text{ }m/s on rails which are 1.5 m1.5\text{ }m apart. To negotiate a curve radius 400 m400\text{ }m, the height by which the outer rail should be raised with respect to the inner rail is (Given, g=g = 10 m/s210\text{ }m/s^{2} ):

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  2. Question 2

    6 Apr 2024

    97
    A car of 800 kg800\text{ }kg is taking turn on a banked road of radius 300 m300\text{ }m and angle of banking 30∘30^{\circ}. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely : (g=10 m/s2,3=1.73)\left( g = 10\text{ }m/s^{2},\sqrt{3}= 1.73 \right)

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