Two spheres of masses m and M are situated in the air and the gravitational force between them is F. The space around the masses in now filled with a liquid of specific density 3. The gravitational force will now be:
Two spheres of masses m and M are situated in the air and the gravitational force between them is F. The space around the masses in now filled with a liquid of specific density 3. The gravitational force will now be:
3F
F
\(\frac{F}{3}\)
\(\frac{F}{9}\)
The Correct Option is B
Solution and Explanation
Gravitational force does not depend on the medium.
In this case time of flight of a ball ≥ 2 × 2 = 4 sec.
∴ Time of flight = 2u/g ≥4
\(\Rightarrow\) u ≥ 2g \(\Rightarrow\) u ≥ 19.6 m/s (∴g = 9.8 m/s2)
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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]