Question

It is known that the time of revolution T of a satellite around the earth depends on the universal gravitational
constant G, the mass of the earth M, and the radius of the circular orbit R. Obtain an expression for T using
dimensional analysis.​

Answer 1

Explanation:

I solve the problem for you my friend please check the answer

Answer 2

Answer: T=$\frac{R}{\sqrt{GM} }$

Explanation:

• The equation for time period is as follows:-

   $T\alpha\ G^{x}M^{y}R^{z}$

⇒$T=k[M^{-1}L^{2}T^{-2} ]M^{y}R^{z}$

⇒$[M^{0}L^{0}T^{-1} ]=k[M^{-x+y}L^{2x+z}T^{-2x} ]$

• Now we compare the powers on both sides of equation,

     -x+y=0 eq(1)

  ⇒x=y      eq(1)

  ⇒2x+z=0 eq(2)

  ⇒-2x=1      eq(3)

• We get x=$\frac{-1}{2}$, y=$\frac{-1}{2}$ and z=1.
• $T= G^{\frac{-1}{2} }M^{\frac{-1}{2} }R^{1}$

     ⇒  $T= \frac{ R}{G^{\frac{1}{2} }M^{\frac{1}{2} }}$

    ∴ T=$\frac{R}{\sqrt{GM} }$

• Hence, the above expression is the required answer.

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