Gravitation

According to the law of gravitation, the force of attraction actingbetween two bodies is given by,

Thus, when the distance between the objects is reduced to half the gravitational force increases by four times the original force.

Let F be the gravitational force acting on a body of mass m, then it can be given by,

From the above equations we can see that F α m, although g (acceleration due to gravity) does not depend on m. Hence, all bodies fall with the same acceleration provided there is no air or other resistance.

Given that, Mass of the body (m) = 1 kg
Mass of the Earth (M) = 6 x 1024 kg
Radius of the earth (R) = 6.4 x 106 m
Now magnitude of the gravitational force (F) between the earth and the body can be given as,

The earth surface attracts the moon with the same force with which the moon attracts the earth. According to Newton’s 3rd law, these two forces are equal and opposite. Also by the universal law of gravitation, the force acting between earth and moon will be:

Where M1 = Mass (earth), M2 = Mass (moon), d = Distance between earth and moon. The magnitude of force (F) is same for earth and moon.

According to the Newton’s 3rd law of motion, the moon also attracts the earth with a force equal to that with which the earth attracts the moon. Since the earth is much larger than the moon so, the acceleration produced on the earth surface (acceleration α 1/m) can not be noticed.

1. When the mass of either body is doubled, the force is also doubled as per the following equation:
   
2. When the distance between the objects is doubled, the force becomes one fourth of the original force as per the following equation:
   
   Similarly it can be shown that when the distance between the objects is tripled, the force becomes one ninth of the original force.
3. In the same way as given in the answer (i) above this can be shown that when the masses of both bodies are doubled, the force becomes four times the original force.

There are many importance of Universal Law of Gravitation as with the help of this law we can explain natural phenomena such as,

1. the force of attraction that binds us to the earth,
2. the motion of planets moving around the sun,
3. the motion of moon around the earth
4. the occurring of tides due to sun and moon.

It is the acceleration produced when a body falls under the influence of the force of gravitation of the earth alone. On the surface of the earth its value is 9.8 m/s2.

Weight of that object.

His friend won’t agree with the weight of gold bought. Since the value of g is less at the equator than that at the poles so, the same gold weighed at the poles will measure less when taken to equator

Because the sheet of paper will experience larger air resistance due to its larger surface area than its surface area in ball form. Hence, a sheet of paper falls slower than one that is crumpled into a ball.

Given that, u = 0, g = 9.8 ms–2, s = 19.6 m
Now, v2 - u2 = 2gs
or, v2 - 0 = 2 x 9.8 x 19.6 = (19.6)2
or, v = 19.6 ms–1 (we will consider value of v only +ve since it is in the downward direction)

Given that, u = 40 ms–1, g = –10 ms–2
At the highest point (h) the velocity (v) will be zero.
using the equation, v2 - u2 = 2gh
0 – 402 = 2(–10)h
or, h = 80 m
or, the total distance covered = 2h = 160 m
Net displacement = 80 – 80 = 0

The buoyant force acts on an object in the vertically upward direction through the center of gravity of the displaced liquid.

It is because the upthrust or the buoyant force exerted by the water brings the plastic block to the surface of water.

Given the mass of the substance = 50 g
Volume of the substance = 20 cm3
Density of substance = Mass ÷ Volume = (50 ÷ 20) g/cm3 = 2.5 g/cm3
Since the density of the substance is greater than the density of water (1 g/cm3), so the substance will sink in the water.

Mass of packet = 500 g
Volume of packet = 350 cm3
Density of packet = Mass ÷ Volume = (500 ÷ 350) g/cm3 = 1.43 g/cm3
The sealed packet will sink in the water as its density is more tan that of water.
The volume of water that will be displaced by the packet = 350 cm3
And mass of this displaced water = Volume x Density = 350 x 1 = 350 gm.