Question

Q. If the universal gravitational constant decreases uniformly with time, then the path of earth around sun will be
(1) Same as it was earlier
(2) Spiral of decreasing radius
(3) Spiral of increasing radius
(4) Straight line

•Answer the question with detailed explanation
•No Spamming​

Answer 1

Answer:

$\sf{(3) \ Spiral \ of \ increasing \ radius.}$

$\sf{F=\dfrac{GM_{1}M_{2}}{R^{2}}}$

$\sf{Here, \ F \ is \ the \ force \ of \ attraction}$

$\sf{between \ two \ bodies,}$

$\sf{M_{1} \ and \ M_{2} \ are \ masses \ of }$

$\sf{two \ bodies \ and \ R \ is \ the \ distance}$

$\sf{between \ them.}$

________________________________

$\sf{If \ the \ universal \ gravitational \ constant}$

$\sf{decreases \ uniformly \ with \ time.}$

$\sf{Since, \ F\propto \ G}$

$\sf{The \ force \ of \ attraction \ between}$

$\sf{sun \ and \ earth \ will \ also \ decrease.}$

$\sf{But, \ F\propto \ \dfrac{1}{R^{2}}}$

$\sf{Since, \ force \ is \ inversely \ proportional}$

$\sf{to \ radius, \ it \ will \ increase \ if}$

$\sf{force \ decrease.}$

$\sf{Hence, \ the \ path \ will \ spiral \ of \ increasing}$

$\sf{radius.}$

________________________________

$\sf\blue{More \ information:}$

$\sf{If \ G \ (gravitational \ constant)}$

$\sf{becomes \ zero, \ then \ the \ revolution}$

$\sf{and \ rotation \ of \ planets}$

$\sf{will \ stop.}$

Answer 2

Answer -

Option C , a spiral of increasing radius .

Solution -

Here , the universal gravitational constant G decreases uniformly with time .

G , generally taken as a constant , is however directly proportional to the gravitational force between any two objects .

Now , here the value of G decreases .

Thus , the magnitude of the gravitational force between the Earth and the Sun will increase .

This will lead to a spiral of a larger radius being formed as the orbit when the earth revolves around the sun .

The figure of revolution of the earth around the sun for this case is included in the attachment .

Finally , if the value of G decreases to become negligible , the earth will overcome the gravitational force of the sun and escape from the orbit.

______________________________________