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Suppose universal gravitational constant...

Suppose universal gravitational constant starts to decrease, then

A

length of the day, on earth, will decrease

B

length of the year will decrease

C

earth will follow a spiral path of increasing radius

D

kinetic energy of earth will decrease

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
Time period, `T = (2 pi r)/(upsilon) = (2pi r)/(sqrt(GM//r)) = (2pi r^(3//2))/((GM)^(1//2))`
i.e., `T prop 1//(G)^(1//2)`
If `G` is decreasing with time, then `T` increases, i.e., earth takes longer time for one revolution. Due to it, the lenght of day, on earth, will decreases. but the lenght of year will increase w.r.t. the original year of earth. The centripetal force on satellite
`F = (m upsilon^(2))/(r ) = (mGM//r)/(r ) = (GMm)/(r^(2))`
As `G` decreases with time, `F` also decreases with time so the earth will move away and describes a spiral path of increasing radius
Kinetic energy, `E_(K) = (1)/(2) m upsilon^(2) = (1)/(2)m (GM)/(r )`
i.e., `E prop G`
so as `G` decreases `KE` decreases.
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