State the Newton’s law of gravitation and express it mathematically. Use this expression to determine what happens to the force between the two objects , if (a) the mass of one object is doubled?
(b) the distance between the objects is tripled?
(c) the mass of both objects are doubled
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Answer:
The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In equation form, this is F=GmMr2 F = G mM r 2 , where F is the magnitude of the gravitational force. G is the gravitational constant, given by G = 6.673 × 10−11 N·m2/kg2.
Explanation:
From the relationship, (i) If the mass of one object (say body 1) is doubled, then Thus, the gravitational force between the two objects gets doubled. (ii) If the distance between the two objects is doubled, then Thus, the gravitational force between the two objects becomes one-fourth.
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If the mass of one of the objects is doubled, then the force of gravity between them is doubled. If the mass of one of the objects is tripled, then the force of gravity between them is tripled. If the mass of both of the objects is doubled, then the force of gravity between them is quadrupled; and so on.
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