The mass of a body is increased 4 times and mass of other body is increased 16 times. how should the distance between them be changed to keep the same gravitational force between them
Answers
Given,
The initial mass of body-1 = M
The final mass of body-1 = 4M
The initial mass of body-2 = m
The final mass of body-2 = 16m
The initial distance between the two bodies = r
Final distance between the two bodies = R
Final gravitational force = Initial gravitational force
To find,
Change in R with respect to r.
Solution,
We can simply solve this numerical problem by using the following process:
As per gravitational law;
The gravitational force acting between two bodies of mass M and m, separated by a distance d, is mathematically represented as;
F = (G ×M×m)/d^2,
where, G = Gravitational constant
= 6.67408 × 10-11 m3 kg-1 s-2
Now, according to the question;
Final gravitational force = Initial gravitational force
=> G (4M×16m)/R^2 = G (M×m)/r^2
=> (4×16) × G (M×m)/R^2 = G (M×m)/r^2
=> R^2/(4×16) = r^2
=> R^2 = (4×16) × r^2 = (2×4)^2 × r^2
=> R = (2×4) × r
=> R = 8r
=> final distance between the two bodies is 8 times the initial distance between the two bodies
Hence, the final distance between the two bodies is 8 times the initial distance between the two bodies.
Answer:
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