JEE Main20244 Apr 2024Evening ShiftPhysicsUnits and DimensionsActual
Applying the principle of homogeneity of dimensions, determine which one is correct, where T is time period, G is gravitational constant, M is mass, r is radius of orbit.
Options
- AT^2= 4 ^2 r^2 G M
- BT^2= 4 ^2 r G M^2
- CT^2= 4 ^2 r^3 G M
- DT^2=4 ^2 r^3
Correct answer
C. T^2= 4 ^2 r^3 G M
Step-by-step solution
According to principle of homogeneity dimension of LHS should be equal to dimensions of RHS so option (3) is correct. aligned & T ^2= 4 ^2 r ^3 GM & [ T ^2 ]= [ L ^3 ] [ M ⁻¹ ~L ^3 ~T ⁻² ][ M ] aligned (Dimension of G is [ M ⁻¹ ~L ^3 ~T ⁻² ] ) [ T ^2 ]= [ L ^3 ] [ L ^3 ~T ⁻² ] = [ T ^2 ]