Question

Using the principle of homogeneity of dimensions, find which of the following is correct: (i) T 2 = 4π 2 r 2

Answer 1

Answer:

please corporate

Explanation:

ANSWER

T

2

=

GM

4π

2

r

3

Taking dimensions on both sides, we get

[T]

2

=

[M

−1

L

3

T

−2

M]

[L]

3

=[M

0

L

0

T

2

]

∴LHS=RHS

Now, T

2

=4π

2

r

2

Taking dimensions on both sides

[T]

2

=[L]

2

∴LHS



=RHS

Now, T

2

=

G

4π

2

r

3

Taking dimensions on both sides

[T]

2

=

[M

−1

L

3

T

2

]

[L]

3

=[M

1

L

0

T

−2

] ∴LHS



=RHS

Now, T=

G

4π

2

r

3

[T]=

[M

−1

L

3

T

−2

]

[L]

3

=[ML

0

T

2

] ∴LHS



=RHS