Question: What is the SI unit of g? A. \[\dfrac{\text{m}}{{{\text{s}}^{\text{2}}}}\] B. \(\dfrac{\text{...

Question

What is the SI unit of g?

A. $\dfrac{\text{m}}{{{\text{s}}^{\text{2}}}}$
B. $\dfrac{\text{m}}{{{\text{s}}^{\text{2}}}}$
C. $\dfrac{s}{{{m}^{2}}}$
D. $\dfrac{\text{m}}{\text{s}}$

Answer 1

Solution

Hint: Convert the mathematical formula of acceleration due to gravity into basic units in the MKS system. Use the basic definition of acceleration due to gravity to find the relationship between the basic quantities that contribute to the formula of g.

Complete step by step answer:
The International System of Units (SI) is the modern form of the metric system. It is the only system of measurement with official status in nearly every country in the world. It comprises a coherent system of units of measurement starting with seven base units.

Second (the unit of time with the symbol s),
Meter (length, m),
Kilogram (mass, kg),
Ampere (electric current, A),
Kelvin (thermodynamic temperature, K),
Mole (amount of substance, mol)
Candela (luminous intensity, cd).

The acceleration which is gained by an object because of gravitational force is called its acceleration due to gravity. The acceleration due to gravity at the surface of Earth is represented by g. Acceleration due to gravity is a vector, which means it has both a magnitude and a direction.

Now unit of g (acceleration) can be calculated as

$\text{a=}\dfrac{\text{ }\\!\\!\Delta\\!\\!\text{ v}}{\text{ }\\!\\!\Delta\\!\\!\text{ t}}$

Where,

$\text{a=}\dfrac{\dfrac{\text{m}}{\text{s}}}{\text{s}}\text{=}\dfrac{\text{m}}{{{\text{s}}^{\text{2}}}}$ = change in velocity

$\text{ }\\!\\!\Delta\\!\\!\text{ t}$ =time

$\text{a=}\dfrac{\dfrac{\text{m}}{\text{s}}}{\text{s}}\text{=}\dfrac{\text{m}}{{{\text{s}}^{\text{2}}}}$

So correct option is (a)

Additional Information: The value of the acceleration due to gravity, g, changes from place to place on the earth. The factors affecting the value of g are the shape of the earth, rotation speed of earth, altitude and depth below the earth's surface.

Note: Acceleration due to gravity, g, essentially has the same unit as that of acceleration. If you are not able to recall the formula for g, you can work in terms of acceleration. As done in the solution.