Question

The dimensional formula for time t, in terms of universal constants c, G and h is??​

Answer 1

Answer:

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Explanation:

Speed of light C=[LT

−1

]

gravitational constant G=[M

−1

L

3

T

−2

]

planck's constant h=ML

2

T

−1

Let M=C

x

G

y

h

z

[M]=[LT

−1

]

x

[M

−1

L

3

T

−2

]

y

[ML

2

T

−1

]

z

[M]=[M

−y+z

L

x+3y+2z

T

−x−2y−z

]

−y+z=1,x+3y+2z=0,−x−2y−z=0

On solving, we get

x=

2

1

;y=

2

−1

;z=

2

1

So, dimension of M=[C

1/2

G

−1/2

h

1/2

]

Answer 2

Explanation:

Here,

[

c

]

=

L

T

−

1

[

G

]

=

M

−

1

L

3

T

−

2

[

h

]

=

M

1

L

2

T

−

1

Let

m

α

c

x

G

y

h

z

By substituting the dimensions of each quantity in both the sides,

M

=

(

L

T

−

1

)

x

(

M

−

1

L

3

T

−

2

)

y

(

M

L

2

T

−

1

)

z

M

=

[

M

y

+

z

L

x

+

3

y

+

2

z

T

x

−

2

y

−

z

]

By equating the power of M, L, T in both the sides:

−

y

+

z

=

1

,

x

+

3

y

+

2

z

=

0

,

−

x

−

2

y

−

z

=

0

By soling the above equation ,

We get,

x

=

1

2

,

y

=

−

1

2

,

and

z

=

1

2

So,

[

m

]

=

c

1

2

G

−

1

2

h

1

2

In above Manner, solve for Length And Time.