Question

If G is the universal gravitational constant , M is the mass of earth R is the radius of earth and h is the altitude then dimension of time is. ​

Answer 1

Answer:

Gravitational force acting between two objects of masses m  

1

​

 and m  

2

​

 separated by distance r, F=  

r  

2

 

Gm  

1

​

m  

2

​

 

​

 

⟹ G=  

m  

1

​

m  

2

​

 

Fr  

2

 

​

 

Thus dimensional formula of G is  

[M]  

2

 

[MLT  

−2

][L]  

2

 

​

 

⟹ G=M  

−1

L  

3

T  

−2

 

Explanation:

Answer 2

Answer:

The dimension of time in terms of M,L and G is $T =M^{-\frac{1}{2} }L^{\frac{3}{2} }G^{-\frac{1}{2} }$.

Explanation:

Given that G is the universal gravitational constant , M is the mass of earth R is the radius of earth which has a dimension of length and h is the altitude which also has dimension of length.

The Universal gravitational constant G has dimensional formula as,

$G=[M^{-1}L^{3} T^{-2} ]$

On rearraging it we get,

$T^{2} =M^{-1} L^{3} G^{-1}$

On solving for the dimensions of T we get,

$T =M^{-\frac{1}{2} }L^{\frac{3}{2} }G^{-\frac{1}{2} }$

Hence, The dimension of time in terms of M,L and G is $T =M^{-\frac{1}{2} }L^{\frac{3}{2} }G^{-\frac{1}{2} }$