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Gravitation

Question
CBSEENPH11020479
Wired Faculty App

If g is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is

  • 2 mgR

  • mgR/2

  • mgR/4

  • mgR

Solution

B.

mgR/2

Gravitational potential energy of body on earth's surface
straight U space equals space minus space fraction numerator GM subscript straight e straight m over denominator straight R end fraction
At a height h from earth's surface, its value is
straight U subscript straight h space equals space minus space fraction numerator GM subscript straight e straight m over denominator left parenthesis straight R plus straight h right parenthesis end fraction space equals space fraction numerator GM subscript straight e straight m over denominator 2 straight R end fraction
where Me = mass of earth
m = mass of body
R = radius of earth
therefore comma space Gain space in space potential space energy space equals space straight U subscript straight h minus straight U equals space fraction numerator negative space GM subscript straight e straight m over denominator 2 straight R end fraction minus open parentheses fraction numerator GM subscript straight e straight m over denominator straight R end fraction close parentheses space equals space fraction numerator GM subscript straight e straight m over denominator 2 straight R end fraction space plus space fraction numerator GM subscript straight e straight m over denominator straight R end fraction space equals space fraction numerator GM subscript straight e straight m over denominator 2 straight R end fraction space equals space fraction numerator gR squared straight m over denominator 2 straight R end fraction space space open parentheses straight g space equals space GM subscript straight e over straight R close parentheses space equals space 1 half space mgR

Some More Questions From Gravitation Chapter

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:

Two 20 g flatworms climb over a very thin wall, 10 cm high. One of the worms is 20 cm long, the other is wider and only 10 cm long. which of the following statement is correct regarding them?

A rocket is intended to leave the Earth's gravitational field. The fuel in its main engine is a little less than the amount that is necessary and an auxiliary engine, (only capable of operating for a short time) has to be used as well. When is it best to switch on the auxiliary engine?

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