Question

4. The gravitational force between two objects is F. How will this force change when i) Distance between them is reduced to half? ii) The mass of each object is 4 quadruplet?

Answer 1

Answer:

Explanation:

If the mass of both of the objects is doubled, then the force of gravity between them is quadrupled; and so on.

... If the separation distance between two objects is doubled (increased by a factor of 2), then the force of gravitational attraction is decreased by a factor of 4 (2 raised to the second power).

Answer 2

The force change when

i) Distance between the two objects is reduced to half, then the force increases by 4 times.

ii) The mass of each two objects is 4 quadruplets, then the force increases by 16 times.

Given:

The gravitational force between two objects of two different masses is F

To Find:

The force change when

i) Distance between the two objects is reduced to half

ii) The mass of each two objects is 4 quadruplet

Solution:

The gravitational force between two objects of mass m1 and m2 is F.

According to Newton's law of gravitation

$F=\frac{Gm_{1} m_{2}}{r^{2} }-----------(1)$

i) When the distance between the two objects is reduced to half

$F_{1} =\frac{Gm_{1} m_{2}}{(\frac{r}{2})^{2} }\\F_{1} = \frac{4Gm_{1} m_{2}}{r^{2} } ---------(2)$

Equation (2) by Equation (1)

$\frac{F_{1} }{F} = \frac{\frac{4Gm_{1} m_{2}}{r^{2} } }{\frac{Gm_{1} m_{2}}{r^{2} } } \\\\\frac{F_{1} }{F} = \frac{4}{1} \\\\F_{1} = 4* F$

Hence, When the distance between the two objects is reduced to half, the force increases by 4 times.

ii) The mass of each two objects is 4 quadruplet

$F_{2} =\frac{G4m_{1}* 4m_{2}}{r^{2} } \\\\F_{2} = \frac{16 Gm_{1}m_{2}}{r^{2} } ----------(3)$

Equation (3) by Equation (1)

$\frac{F_{1} }{F} = \frac{\frac{16Gm_{1} m_{2}}{r^{2} } }{\frac{Gm_{1} m_{2}}{r^{2} } } \\\\\frac{F_{1} }{F} = \frac{16}{1} \\\\F_{1} = 16* F$

When The mass of each object is 4 quadruplets, the force increases by 16 times.

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