What happens to the magnitude of the force of gravitation between two
objects if
(i)distance between the objects is tripled?
(ii)mass of both objects is doubled?
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What happens to the magnitude of the force of gravitation between two
objects if
(i)distance between the objects is tripled?
(ii)mass of both objects is doubled?
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Answer:
The force of gravitation between two objects is described by Newton's law of universal gravitation, which states:
F = (G * m1 * m2) / r^2
Where:
- F is the force of gravitation between the two objects.
- G is the gravitational constant (a constant value).
- m1 and m2 are the masses of the two objects.
- r is the distance between the centers of the two objects.
Let's consider the two scenarios:
(i) If the distance between the objects is tripled (r is tripled):
When the distance (r) between the objects is tripled, it appears in the denominator of the formula as r^2. Since r^2 is proportional to the square of the distance, if you triple the distance, r^2 becomes 9 times larger. As a result, the force of gravitation between the two objects will decrease to 1/9th of its original value. So, the force decreases significantly.
(ii) If the mass of both objects is doubled (m1 and m2 are both doubled):
When the masses of both objects are doubled, they appear in the formula as m1 and m2. Since these masses are in the numerator, if you double both of them, the force of gravitation between the objects will increase by a factor of 2 * 2 = 4. So, the force becomes four times its original value.
In summary:
(i) If the distance between the objects is tripled, the force of gravitation decreases to 1/9th of its original value.
(ii) If the mass of both objects is doubled, the force of gravitation increases to 4 times its original value.