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Journey to the Center of the Earth - What Lies inside it?

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The gravitational force on a body inside the surface of the earth varies as ra, where r is the distance from the center of the earth and a is some constant. If the density of the earth is assumed uniform, then -

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If an artificial statellite is orbiting the earth, it it possible for the plane of the orbit to not pass through the center of the earth? On what property of the gravitational force is your answer based?

Two mass m_(1)&m_(2) are initially placed at rest inside two smooth tunnels in earth as shown in the figure. The minimum distance between the tunnels and the center of earth R/2 as shown in the figure. Then

(a) What will an object weigh on the Earth's surface if it weighs 160 N on the Moon's surface? (b) How many Earth radii must this same object be from the center of Earth if it is to weigh the same as it does on the Moon?

It is known that if the length of the day were T0 hour, a man standing on the equator of the earth would have felt weightlessness. Assume that a person is located inside a deep hole at the equator at a distance of (R)/(2) rom the centre of the earth. What should be the time period of rotation of the earth for such a person to feel weightlessness? [R = radius of the earth]

If d is the distance from a point P to the center of the circle of radius r and d-r gt0 , then the point P lies………… the circle. (outside/inside/on)

A ball is released in a smooth dimetrical tunnel of earth a. After how much time will it pass through the center of earth? b. With what speeed will the ball pass the center earth?

Assuming that the earth radius is 6400 km and that it subtends an angle of 57 at the center of the moon from the earth. find the distance between earth and moon center.

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