AP EAMCET202421 May 2024Morning ShiftPhysicsUnits and DimensionsActual
The time period of revolution of a satellite ( T ) around the earth depends on the radius of the circular orbit ( R ), mass of the earth (M) and universal gravitational constant (G). The expression for T , using dimensional analysis is ( K is constant of proportionality)
Options
- AK R ^2 GM
- BK R G M
- CK R ^3 GM
- DK R ^3 GM ^2
Correct answer
C. K R ^3 GM
Step-by-step solution
aligned & T R ^ a M ^ b G ^ c T = k R ^ a M ^ b G ^ c & [ T ]=[ L ]^ a [ M ]^ b [ M ⁻¹ ~L ^3 ~T ⁻² ]^ c & a +3 c =0 & ~b - c =0 ~b = c & -2 c =1 c =- 1 2 & a +3 (- 1 2 )=0 a = 3 2 & ~T = KR ^ 3 2 M ^ - 1 2 G ^ - 1 2 = K R ^3 GM aligned