NEET > Test: Universal Law of Gravitation

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Test: Universal Law of Gravitation - Question 1

SI unit of gravitational constant is __________.

Detailed Solution for Test: Universal Law of Gravitation - Question 1

We know that:

Thus we get, [G] = [F.R^{2} / m^{2} ] = [F] x L^{2} x M^{-2 }= [F] M^{-2} L^{2 }= N kg^{-2} m^{2}

Detailed Solution for Test: Universal Law of Gravitation - Question 2

From Newton’s law of gravitation,

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

∴ The dimensional formula of force = M^{1} L^{1} T^{-2}

⇒ Gravitational Constant (G) = F × r^{2} × [m_{1}m_{2}]^{-1}

Or, G = [M^{1} L^{1} T^{-2}] × [L]^{2} × [M]^{-2} = [M^{-1} L^{3} T^{-2}].

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

Detailed Solution for Test: Universal Law of Gravitation - Question 3

**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.

Test: Universal Law of Gravitation - Question 4

Two bodies with same mass “m” separated by a distance “r” exert a gravitational force of F on each other. Suppose the distance between them is doubled and the force becomes F’. The ratio of two forces is

Detailed Solution for Test: Universal Law of Gravitation - Question 4

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

Test: Universal Law of Gravitation - Question 5

The mass of the body on moon is 40kg, what is the weight on the earth.

Detailed Solution for Test: Universal Law of Gravitation - Question 5

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

Detailed Solution for Test: Universal Law of Gravitation - Question 6

The value of G is universally constant = 6.67 × 10^{-8} dyne.cm^{2}/g^{2}

__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} Nm^{2}/kg^{2} = 6.67 × 10^{-8} { 10^{-5}× 10^{-4} /10^{-6}} Nm^{2}/kg^{2}

= 6.67 × 10^{-8} × 10^{-3} N.m^{2}/kg^{2}= 6.67× 10^{-11} Nm^{2}/kg^{2}

Detailed Solution for Test: Universal Law of Gravitation - Question 7

- 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**.

Test: Universal Law of Gravitation - Question 8

G is a universal gravitational constant, its value is:

Detailed Solution for Test: Universal Law of Gravitation - Question 8

__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. Nm^{2} /kg^{2}

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

Test: Universal Law of Gravitation - Question 9

In orbit, objects inside a spacecraft feel weightless:

Detailed Solution for Test: Universal Law of Gravitation - Question 9

- 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.

Detailed Solution for Test: Universal Law of Gravitation - Question 10

**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.**

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