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A tunnel is dug along a chord of the earth at a perpendicular distance R2 from the centre of earth. The wall of the tunnel may be assumed to be frictionless. A particle is released from one end of the tunnel. The pressing force by the particle on wall is depicted by the graph

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Important Questions on Gravitation

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A particle of mass m is subjected to an attractive central force of magnitude kr2,k being a constant. At the instant when the particle is at its extreme position in its closed orbit at a distance a from the centre of force, its speed is k2ma. If the distance of other extreme is b, find ab.
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The percentage change in the acceleration of the Earth towards the Sun from a total eclipse of the Sun to the point where the Moon is on a side of Earth directly opposite to Sun is
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The escape velocity for a body projected vertically upwards is 11.2 km s-1. If the body is projected in a direction making an angle 45° with vertical, the escape velocity will be,
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For a particle projected in a transverse direction from a height h above earth's surface, find the minimum initial velocity so that it grazes the surface of earth such that path of this particle would be an ellipse with centre of earth as the farther focus, point of projection as the apogee and a diametrically opposite point on earth as perigee.
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A particle is dropped on Earth from height R (radius of earth) and it bounces back to height h. If the coefficient of restitution of collision is 23, then find h.
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A uniform spherical planet (radius R) has acceleration due to gravity at its surface as g. Points P and Q located inside and outside the planet, respectively have acceleration due to gravity g4. Maximum possible separation between P and Q is
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A comet is moving around the earth in highly elliptical orbit. Identify the incorrect statement.
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Two particles are projected from the surface of the earth with velocities 57gR and 25gR where, R is the radius of the earth. What would be the ratio of maximum heights attained?