Question:
Two lead balls of masses m and 5m having radii R and 2R are separated by 12R, If they attract.each other by gravitational force, the distance covered by small sphere before they touch each other is
Two lead balls of masses m and 5m having radii R and 2R are separated by 12R, If they attract.each other by gravitational force, the distance covered by small sphere before they touch each other is
Updated On: Jan 8, 2024
- 10 R
- 7.5 R
- 9 R
- 2.5 R
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The Correct Option is B
Solution and Explanation
Effective distance =9R
Distance travelled by Smaller mass= x
$x = \left(\frac{m_2}{m_1 + m_2 }\right) (9R)$
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Concepts Used:
Newtons Law of Gravitation
Gravitational Force
Gravitational force is a central force that depends only on the position of the test mass from the source mass and always acts along the line joining the centers of the two masses.
Newton’s Law of Gravitation:
According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,
- Directly proportional to the product of their masses i.e. F ∝ (M1M2) . . . . (1)
- Inversely proportional to the square of the distance between their center i.e. (F ∝ 1/r2) . . . . (2)
By combining equations (1) and (2) we get,
F ∝ M1M2/r2
F = G × [M1M2]/r2 . . . . (7)
Or, f(r) = GM1M2/r2 [f(r)is a variable, Non-contact, and conservative force]