Question

Example 1.2 The value of gravitational constant G in MK
system is 6.67x10-11 N-m2 kg-2. What will be its value
CGS.​

Answer 1

Explanation:

Dimensional formula for G is [M

−1

L

3

T

−2

]

Now, n

1

[M

1

−1

L

1

3

T

1

−2

]=n

2

[M

2

−1

L

2

3

T

2

−2

]

n

2

=n

1

[

M

2

M

1

]

−1

[

L

2

L

1

]

3

[

T

2

T

1

]

−2

Here, n

1

=6.67×10

−11

M

1

=1kg, M

2

=1g=10

−3

kg, L

1

=1m, L

2

=1cm=10

−2

m, T

1

=T

2

=1s

Substituting in above equation we get,

n

2

=6.67×10

−11

[

10

−3

kg

1kg

]

−1

[

10

−2

m

1m

]

3

[

1s

1s

]

−2

or, n

2

=6.67×10

−8

Thus, value of G in CGS units is 6.67×10

−8

dynecm

2

/g

2

.

Answer 2

G=6.67+10^-11 N-m^2 / m^2 kg^2

=6.67×10^-11×(10^5dyne)(10^4)cm^2 / (10^3g)^2

=6.67×10^-11×10^5×10^4×10^3 / 10^6

G=6.67×10^-8 dyne cm^2/gm^2