Option 2 : is reduced to quarter
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CONCEPT:
- Newton's Law of Gravitation: According to Newton's law of gravitation, the gravitational force acting between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
- Mathematically, the gravitational force between two objects is given as
\(F = G\frac{m_1m_2}{r^2}\)
G is the Universal Gravitational Constant. which is the same throughout the universe. m1 and m2 are two masses, r is the distance between two masses, F is the gravitational force between m1 and m2
CALCULATION:
So, the Gravitational force between two masses m1 and m2 at distance r is
\(F = G\frac{m_1m_2}{r^2}\) -- (1)
If the distance is doubled, the new distance is
r' = 2r
and new force s F'
\(F' = G\frac{m_1m_2}{r'^2}\)
\(F'= G\frac{m_1m_2}{(2r)^2}\)
\(F' = G\frac{m_1m_2}{4r^2}\)
\(F'=\frac{1}{4} G\frac{m_1m_2}{r^2}\)
\(F'=\frac{F}{4}\) (Using Equation 1)
So, F' = F / 4
So, the gravitational force becomes one-fourth or quarter of the original value.
Additional Information
The value of universal Gravitational constant (G) is
G = 6.674×10−11 m3 kg−1 s−2
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