Question

Explain Newtons law of gravitation. Define gravitational constant and give its dimensional formlla? (5 marks)​

Answer 1

Answer:

Newton's Law of Gravitation states that :

Force between 2 bodies :

• is directly proportional to the product of the masses of the bodies.
• inversely proportional to the square of the Distance between the bodies.

Mathematically :

$1. \: f \: \propto \: (m1 \times m2)$

$2. \: f \: \propto \: (\dfrac{1}{ {r}^{2} } )$

Combining the two proportionals :

$\therefore \: f \: \propto \: \dfrac{m1 \times m2}{ {r}^{2} }$

Inserting an constant :

$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \sf{ \red{f = G \dfrac{(m1 \times m2)}{ {r}^{2} }}}}$

Universal Gravitational Constant :

It is numerically equal to the force existing between 2 unit masses located at a unit distance from one another.

$\therefore \: G = (\dfrac{f \times {r}^{2} }{m1 \times m2 } )$

$\therefore \: G = \{\dfrac{ML {T}^{ - 2} \times {L}^{2} }{ {M}^{2}} \}$

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

Answer 2

Dimensional Formula of Gravitational Constant

The dimensional formula of gravitational constant is given by,

M-1 L3 T-2

Where,

M = Mass

L = Length

T = Time

Derivation

From Newton’s law of gravitation,

Force (F) = [GmM] × r-2

Gravitational Constant (G) = F × r2 × [Mm]-1  . . . . (1)

Since, Force (F) = Mass × Acceleration = M × [LT-2]

∴ The dimensional formula of force = M1 L1 T-2 . . . . (2)

On substituting equation (2) in equation (1) we get,

Gravitational Constant (G) = F × r2 × [Mm]-1

Or, G = [M1 L1 T-2] × [L]2 × [M]-2 = [M-1 L3 T-2].

Therefore, the gravitational constant is dimensionally represented as M-1 L3 T-2