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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

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`From = F = (Gm_1 m_2)/(r^2)`
`G =(F r^2)/(m_1 m_2) = (MLT^(-2)(L^2))/(M^2) = [M^(-1) L^3 T^(-2)]`
`G = 6.67xx10^(11) kg^(-1) m^3 s^(-2)`
`= 6.67xx10^(11) (10^3g)^(-1) (10^2cm)^3 s^(-2)`
`=6.67xx10^(14)g cm^3 s^(-2)`
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Knowledge Check

  • The SI unit of the universal gravitational constant G is

    A
    Nm `kg^(–2)`
    B
    `Nm^(2)kg^(–2)`
    C
    `Nm^(2) kg^(–1)`
    D
    Nm`kg^(–1)`

  • The value of universal gravitational constant 'G' is

    A
    `6.67 xx 10^(11) Nm^2 // Kg^2`
    B
    `6.67 xx 10^(-11) Nm^2 //Kg^2`
    C
    `6.67 xx 10^(18) Nm^2 // Kg^2`
    D
    `6.67 xx 10^(-18) Nm^2 // Kg^2`

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

    A
    `dy"ne"cm^2//g^2`
    B
    `dy"ne"g^2//cm^2`
    C
    `dy"ne"^2cm//g`
    D
    `g^2//dy"ne"cm^2`

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