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Gravitation

Question

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The height at which the acceleration due to gravity becomes g/9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is

2R

$fraction numerator straight R over denominator square root of 2 end fraction$

R/2

$square root of 2 straight R end root$

Solution

A.

2R

fraction numerator GM over denominator 9 straight R squared end fraction space equals space fraction numerator GM over denominator left parenthesis straight R plus straight h right parenthesis squared end fraction rightwards double arrow space 3 straight R space equals space straight R plus straight h rightwards double arrow space straight h equals space 2 straight R

Some More Questions From Gravitation Chapter

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected?

Which of the following statements is correct?
(a) Centre of the mass of a body always coincides with the centre of gravity of the body.
(b) Centre of the mass of a body is the point at which the total gravitational torque on the body is zero
(c) A couple on a body produce both translational and rotational motion in a body.
(d) Mechanical advantage greater than one means that small effort can be used to lift a large load.

Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will:

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