Test: Universal Law of Gravitation

We know that:

Thus we get, [G] = [F.R² / m² ] = [F] x L² x M^-2 = [F] M^-2 L² = N kg^-2 m²

From Newton’s law of gravitation,

Since, Force (F) = Mass × Acceleration = M × [LT^-2]
∴ The dimensional formula of force = M¹ L¹ T^-2

⇒ Gravitational Constant (G) = F × r² × [m₁m₂]^-1
Or, G = [M¹ L¹ T^-2] × [L]² × [M]^-2 = [M^-1 L³ T^-2].

Therefore, the gravitational constant is dimensionally represented as [L]³ [M]^-1 [T]^-2.

Tides refer to the rise and fall of our oceans' surfaces. It is caused by the attractive forces of the Moon and Sun's gravitational fields as well as the centrifugal force due to the Earth's spin.

We know that the force of gravitation is inversely proportional to square of the distance between the two bodies,

i.e. F∝ r^-2

Hence, when the distance between them will be doubled, the force will be reduced by 4 times

So, the ratio will be 4:1

Weight = Mass * Accelertion due to gravity = 40 * 9.8 = 392 N

The value of G is universally constant = 6.67 × 10^-8 dyne.cm²/g²

We know:
1 dyne = 10^-5 N
1 cm = 10^-2 m
1 g = 10^-3 kg

⇒ 6.67 × 10^-8 × ( 10^-5) .(10^-2)²/(10^-3)² Nm²/kg² = 6.67 × 10^-8 { 10^-5× 10^-4 /10^-6} Nm²/kg²
= 6.67 × 10^-8 × 10^-3 N.m²/kg²= 6.67× 10^-11 Nm²/kg²

• Gravitational force strictly follows Newton’s Third Law of motion i.e. for every action force there is an equal and opposite reaction force.
• Gravitational forces add up like vectors i.e. they obey the principle of superposition.

We know that: [g] = [G.m.m / r.r]
Since the unit of G must be same as the unit of g.r.r / m.m  i.e. Nm² /kg²

Also, we know that G is very very less than 1 as the gravitational force is a very weak force.

• Astronauts float around in space because there is no gravity in space.
• Astronauts are so far from the Earth that gravity is so small. This is why NASA calls it microgravity.

The gravitational force of the earth acts on every object having mass. When a ball is thrown upwards the gravitational force of the earth acts against the velocity of the object and pulls the ball downwards, i.e, towards itself.

Thus, gravity pulls a ball back to earth.