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Equations of motion of an object under free fall:

The initial velocity of the object remains zero when the object is under free fall. In this situation, the three equations of motion i.e. v = u + gt

s = ut + gt

v² = u² + \(\frac{1}{2}\) gt²

v² = u² + 2gh will become,

ν = gt

s = \(\frac{1}{2}\)gt² and v² = 2gh

Here, u = final velocity, t = time, g = acceleration due to gravity, h = height attained by the body.

Mass of the object on earth is 12 kg. It will be 12 kg on the moon also. Value of ‘g’ on the moon is one-sixth of its value on the earth.

Weight of the object on earth = mg = 12 x 9.8 = 117.6

N Weight of the object on moon 1

= 12 x \(\frac{1}{2}\) x 9.8 = 19.6 N.

The acceleration produced in a body due to the gravitational pull of the earth, near its surface is called acceleration due to gravity. It is denoted by ‘g’. i.e., 

\(g=\frac{G.M_e}{R^2_e}\)

Here, M_e = mass of earth, R_e = radius of earth and G is universal gravitational constant.

The force exerted by the earth and the moon on each other is insufficient to move the earth, on account of its huge mass.

1. Any two objects in the universe attract each other by a force called gravitational force. 

2. It produces almost negligible acceleration. 

3. It is not the measure of weight, g (gravity) 

4. The force of gravitation exerted by the earth is called gravity. 

5. Gravity causes the object to accelerate. It measures the weight, i.e., w = mg.

When d is doubled, the gravitational force will become one fourth.

The answer is (A) have the same velocity at any instant

The answer is (B) the mass of a body is not zero but the weight is zero

The earth and the moon pull each, other due to the gravitational force of attraction. Water on the earth (ocean) is attracted by both the earth and the moon. The molecules in water are not rigidly fixed. Therefore, when the moon and the sun both lie on the same side of the earth (new moon) or on the opposite side of the earth (full moon) with the ocean, the combined gravitational pull causes a bulge in the ocean water. This bulging out of the ocean water in the direction of the moon is called tide.

The value of g varies from point to point in the universe, according to the values of M and r. Since the earth is flattened at poles and V reduces. Now since \(g\alpha \frac{1}{r^2}\). 

Therefore, the value of g is more at poles of the earth than the equator.

The answer is (C) any two massive bodies

“Every particle in the universe attracts every other particle with a force, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them”.

Mass of the object (m) = 10 kg

Acceleration due to gravity on earth = g 

acceleration due to gravity on moon = g

Now,

\(g_m=\frac{g_e}{6}=\frac{9.8}{6}=1.635m/sec^2\)

Weight of an object on earth W_e = mg_e = 10 × 9.8 = 98 Newton

Weight of an object on the moon

W_m = mg_m = 10 × 1.635 = 16.35 Newton

The universal law of gravitation successfully explained the planetary motion in our solar system. The gravitational force is responsible for so many natural phenomenon like the formation of tides in seawater, the existence of the atmosphere near the earth and many more.

The earth and the apple move towards each other, but the magnitude of the displacement of the earth is negligible relative to that of the apple. Also the observer is located on the earth.

[Note: The mass of the earth is far greater than that of an apple. Hence, the magnitude of the acceleration of the earth is negligible relative to that of the apple.]

F = ma and F = \(\frac{GMm}{r^2}\)

∴ Acceleration, a = \(\frac{GM}{r^2}\). This is independent of the mass (m) of the object. 

Hence, an object of larger mass and an object of lower mass fall down with the same velocity.

Gravitation: It is the force of attraction between any two bodies in the universe. 

Gravity: It is the force of attraction between the earth and any object lying on or near its surface.

Gravitation is the force of attraction between any two bodies while gravity refers to the force of attraction between any body and the earth.

The gravitational field strength at a point in a field is defined as the force experienced by a body of unit mass placed at that point.

I = \(\frac {GM}{R^2}\) ⇒ I = g

The value of I is maximum for Saturn.

I = \(\frac {300N}{60kg}\)

I = 5 ms^-2.

1 Part: A satellite which revolves round the earth with the same angular speed and the same direction as that of earth around its axis is a geostationary satellite. 

Uses of artificial satellites:

1. for mapping of forests (or to study deforestation) 

2. for mapping of rivers, reservoirs 

3. for pollution monitoring. 

4. for weather forecasting, prediction, and warning of cyclones, mapping of flood-affected areas 

5. geostationary satellites are used for telephones, mobiles, broadcasting of radio and television.

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