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Chapter 6: Problem 671

Two sphere of mass \(\mathrm{m}_{1}\) and \(\mathrm{m}_{2}\) are situated in air and the gravitational force between them is \(F\). The space around the masses is now filled with liquid of specific gravity 3 . The gravitational force will now be (A) \(\mathrm{F}\) (B) \(3 \mathrm{~F}\) (C) \(\mathrm{F} / 3\) (D) \(\mathrm{F} / 9\).

Short Answer

Expert verified
The new gravitational force between the masses in the liquid medium is \(\frac{F}{3}\). So, the correct answer is (C) \(\frac{F}{3}\).

Step by step solution

01

State the formula for gravitational force between two masses.

The formula for the gravitational force between two masses is given by Newton's law of gravitation: \[F = G \frac{m_1 m_2}{r^2}\] Where \(F\) is the force, \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses, and \(r\) is the distance between the centers of the masses.
02

Identify the change in medium properties.

When the medium changes from air to liquid, the specific gravity of the medium is increased to 3. We need to account for this change when calculating the new gravitational force.
03

Relate specific gravity to the actual gravitational force.

Specific gravity is defined as the ratio of the density of the substance to the density of a reference substance. In this case, the reference substance is air, and we assume it has a specific gravity of 1. Therefore, the force \(F\) that we have initially is the actual gravitational force between the masses in air. When the medium changes, the new medium's density will affect how the masses interact gravitationally.
04

Calculate the gravitational force in the liquid medium.

When the medium is changed to a liquid with a specific gravity of 3, the actual gravitational force between the masses becomes: \[F' = \frac{F}{3}\] This is because the denser liquid medium will reduce the apparent masses of the objects due to buoyancy, making them feel lighter, and the force between them will be reduced.
05

Find the correct answer among the given options.

Based on our calculations, the new gravitational force between the masses in the liquid medium is \(\frac{F}{3}\). Therefore, the correct answer is: (C) \(\frac{F}{3}\).

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