Assertion (A): Two identical trains move in o | vedclass

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(D) Let the Earth rotate with angular velocity $\omega$. Let the train move with speed $v$ relative to the Earth's surface.For a train moving in the d

Vedclass · Accepted Answer

$A$ is false,$R$ is false

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(D) Let the Earth rotate with angular velocity $\omega$. Let the train move with speed $v$ relative to the Earth's surface.For a train moving in the direction of the Earth's rotation (West to East),the total angular velocity is $\omega' = \omega + v/R$. The centripetal force required is $F_1 = m(\omega + v/R)^2 R$.For a train moving opposite to the Earth's rotation (East to West),the total angular velocity is $\omega'' = \omega - v/R$. The centripetal force required is $F_2 = m(\omega - v/R)^2 R$.Since $F_1 
eq F_2$,the normal reactions $N_1 = mg - F_1$ and $N_2 = mg - F_2$ are not equal. Thus,Assertion $(A)$ is false.The centripetal acceleration depends on the net angular velocity relative to the inertial frame,not just the speed $v$ relative to the Earth. Thus,Reason $(R)$ is also false.

Assertion $(A):$ Two identical trains move in opposite senses in the equatorial plane with the same speeds relative to the Earth's surface. They have equal magnitude of normal reaction.
Reason $(R):$ The trains have different centripetal accelerations due to different speeds.

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Assertion $(A):$ Two identical trains move in opposite senses in the equatorial plane with the same speeds relative to the Earth's surface. They have equal magnitude of normal reaction.Reason $(R):$ The trains have different centripetal accelerations due to different speeds.