Question

The S.I. unit to C.G.S for gravitational intensity is
(A) ${10^3}:1$
(B) infinity
(C) zero
(D) ${10^2}:1$

Answer 1

Hint
The gravitational intensity refers to the acceleration due to gravity. The SI unit of the acceleration due to gravity is $m/{s^2}$. So by the conversion factor of the S.I. units of the acceleration due to gravity to the C.G.S unit, and then finding the ratio of it to the S.I unit, we get the answer.

Complete step by step answer
The gravitational intensity refers to the acceleration due to gravity. The acceleration due to gravity is the acceleration that is gained by a particle due to the gravitational force of the earth. It is symbolized by the variable, $g$ and the standard value of $g$ above the earth’s sea level is given by $g = 9.8m/{s^2}$ in the S.I. unit. In the C.G.S. unit, the units are given by, $cm/{s^2}$. So to convert the value to the C.G.S. unit, we use the following conversion values,
$1m = 100cm$.
So, we get
$1m/{s^2} = 100cm/{s^2}$.
Therefore, the value of the acceleration due to gravity in the C.G.S. unit is,
$9.8m/{s^2} = 9.8 \times 100cm/{s^2} = 980cm/{s^2}$
Hence, the ratio S.I unit: C.G.S unit is,
$1m/{s^2}:1cm/{s^2}$
That is, $100:1$
So the S.I unit to C.G.S unit of gravitational intensity is ${10^2}:1$
Therefore, the correct answer is option (D).

Additional Information
The value of the acceleration due to gravity is affected by various factors, given by:
- Altitude above the earth’s surface
- Depth below the surface of the earth
- the shape of the earth
- and the rotational motion of the earth.

Note
For the gravitational intensity or the acceleration due to gravity, the dimensional formula is given by ${M^0}{L^1}{T^{ - 2}}$. From here we can see the SI unit of the gravitational intensity will be given by, $m/{s^2}$ and the C.G.S unit is $cm/{s^2}$.