Question

The value of gravitation is G = 6.67 xx 10^(-11)N-m^(2)/kg^(2) in SL units . Convert it into CGS system of units .

Answer 1

Given:-

The value of G = 6.67x10⁻¹¹ N²m²/kg²

To Find:-

Convert given value into CGS system of units.

Solution:-

First we have solve

1N = 10⁵dynes.

1m = 100cm =>  1m² = 10⁴cm².

1kg = 1000g => 1kg² = 10⁶g².

Now using these vale in given value of G, then we have

G = 6.67x10⁻¹¹ Nm²/kg².

or

G = $\frac{6.67x10^{-11}x10^{5}x10^{4} }{10^{6} } dyne.\frac{cm^{2} }{g^{2} }$

By solving above value we get

G = 6.67x10⁻⁸ dyne cm²/g².

i.e G = $6.67x10^{-8} dyne\frac{cm^{2} }{g^{2} }$ ,This is the value of G in terms of CGS system

Answer 2

The value the of G in CGS system of units is = 6.67 × 10^−2 dyne cm^2/g^2

Explanation:

The dimensional formula ofGis [M−1 L^3 T]^−2

Using Equation (a) , l.e.

n1[M1−1 L13 T1−2 ] = n2 [M2−1 L23 T2−2 ]

n2 = [M1 / M2]^−1 [L1 / L2]^3 [T1 / T2]^−2

Here, n1 = 6.67 × 10^−11

M1 = 1 kg

M2 = 1 kg = 10^−3 kg

L = 1 m

l2 = 1 cm= 10^−2m

T1 = T2 = ls

Subsitutiion in the above equation we get

n1 = 6.67 × 10^−11 [ 1 kg / 10^−3 kg]^−1 [1 kg / 10^−3 kg]^3 [1 kg / 10^−3 kg]^−2

or n2 = 6.67 × 10^−2

Thus value the of G in CGS system of units is =6.67×10−2dynecm2/g2