Calculate the dimensions of universal gr...

Calculate the dimensions of universal gravitational constant. If its value is SI units is `6.67xx10^(11),` what will be its value is cgs system ?

Text Solution

Verified by Experts

Dimensional formula of `G= [M^(-1)L^(3)T^(-2)]`
Let `n_(1)" and "n_(2)` are the values of G in MKS and CGS system and let `u_(1)" and "u_(2)` represent MKS and CGS system, respectively.
`n_(1)u_(1)=n_(2)u_(2)`
`implies n_(1)[M_(1)^(-1)L_(1)^(3)T_(1)^(-2)]=n_(2)[M_(2)^(-1)L_(2)^(3)T_(2)^(-2)]`
`implies n_(2)=n_(1)[(M_2)/(M_1)]^(1)[(L_1)/(L_2)]^(3)[(T_2)/(T_1)]^(2)`
`implies n_(2)=(6.67xx10^(-11))[(1g)/(1000g)]^(1)[(100cm)/(1cm)]^(3)[(1s)/(1s)]^(2)`
`implies n_(2)=(6.67xx10^(-11))xx10^(3)`
`implies n_(2)=6.67xx10^(-8)`.

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The SI unit of the universal gravitational constant G is

Nm `kg^(–2)`

`Nm^(2)kg^(–2)`

`Nm^(2) kg^(–1)`

Nm`kg^(–1)`

The value of universal gravitational constant 'G' is

`6.67 xx 10^(11) Nm^2 // Kg^2`

`6.67 xx 10^(-11) Nm^2 //Kg^2`

`6.67 xx 10^(18) Nm^2 // Kg^2`

`6.67 xx 10^(-18) Nm^2 // Kg^2`

The C.G.S. unit of universal gravitational constant is

`dy"ne"cm^2//g^2`

`dy"ne"g^2//cm^2`

`dy"ne"^2cm//g`

`g^2//dy"ne"cm^2`