The bodies of mass 10 kg and 30 kg are
separated by a distance 12 m. The point
between two bodies where the resultant
gravitational force is zero
Answers
Answer:
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Explanation:
Body of a mass =10kg 30kg
Seperated by a distance = 12m
= 10kg 42m
Therefore,the point between two bodies where not the result gravitational force, the exact point was 10kg 42m....
Given : The bodies of mass 10 kg and 30 kg are separated by a distance 12 m.
To Find : The point between two bodies where the resultant gravitational force is zero
Solution:
Let say point is at distance of x m from 10 kg toward 30 kg
hence distance from 30 kg is 12 - x m
Gravitational force between unit mass at the point of 10 kg
= G * 10 * 1 / x²
Gravitational force between unit mass at the point of 10 kg
= G * 30 * 1 / (12-x)²
Equating both
G * 10 * 1 / x² = G * 30 * 1 / (12-x)²
=> (12-x)² = 3x²
=> 144 + x² - 24x = 3x²
=> 2x² + 24x - 144 = 0
=> x² + 12x - 72 = 0
=> x = (- 12 ± √12² - 4(1)(-72) )/2
=> x = -6 ± √(6² + 72)
=> x = - 6 ± 6√3
=> x = 6(√3 - 1) as x can not be - ve as point between bodies to be found
The point between two bodies where the resultant gravitational force is zero is 6(√3 - 1) from 10 kg body
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