Angular speed of rotation of earth is ω0. A train is running along the equator at a speed ‘v’ from west to east with respect to surface of earth. A very sensitive balance inside the train shows the weight of the object as W1. During the return journey when the train is running at same speed from east to west (with respect to surface of earth) the balance shows the weight of the object to be W2. Weight of the object shown by the balance at the poles is W0. The value of W2−W1 was found out to be pW0ω0vg (g is the acceleration due to gravity on the surface of the earth). Find the value of ‘p’?

Question

Angular speed of rotation of earth is ω0. A train is running along the equator at a speed ‘v’ from west to east with respect to surface of earth. A very sensitive balance inside the train shows the weight of the object as W1. During the return journey when the train is running at same speed from east to west (with respect to surface of earth) the balance shows the weight of the object to be W2. Weight of the object shown by the balance at the poles is W0. The value of W2−W1 was found out to be pW0ω0vg (g is the acceleration due to gravity on the surface of the earth). Find the value of ‘p’?

Infinity Learn · Accepted Answer

When train is at rest W0=mg(V0=W0R)When train moves from west to east W1=mg−m(v0+v)2RWhen train moves from east to west W2=mg−m(v0−v)2R⇒W2−W1=mR[(v0+v)2+(v0+v)2] =mR4v0v=4mv0vR=4mv0vR=4W0gW0v

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