What happens to the force between two objects, if
(i) the mass of one object is doubled?
(ii) the distance between the objects is doubled and tripled?
(iii) the masses of both objects are doubled?

Answer

From Universal law of , force exerted on an object of mass m by earth is given by

So as the mass of any one of the object is doubled the force is also doubled

(ii) The force F is inversely proportional to the distance between the objects. So if the distance between two objects is doubled then the gravitational force of attraction between them is reduced to one fourth of its original value. Similarly f the distance between two objects is tripled , then the gravitational force of attraction becomes one ninth of its original value.

(iii) Again fron Universal law of attraction from equation 1 force F is directly proportional to the product of both the masses. So if both the masses are doubled then the gravitational force of attraction becomes four times the original value.

Universal law of Gravitation is important because it it tells us about:
→ the force that is responsible for binding us to Earth.
→ the motion of moon around the earth
→ the motion of planets around the sun
→ the tides formed by rising and falling of water level in the ocean are due to the gravitational force exerted by both sun and moon on the earth.

Acceleration of free fall is the acceleration produced when a body falls under the influence of the force of gravitation of the earth alone. It is denoted by g and its value on the surface of the earth is 9.8 ms^-2.

Gravitational force between the earth and an object is known as the weight of the object.

Weight of a body on the Earth is given by:
W= mg
Where,
m= Mass of the body
g= Acceleration due to gravity
The value of gis greater at poles than at the equator. Therefore, gold at the equator weighs less than at the poles. Hence, Amit's friend will not agree with the weight of the gold bought.

When a sheet of paper is crumbled into a ball, then its density increases. Hence, resistance to its motion through the air decreases and it falls faster than the sheet of paper.

Weight of an object on the moon = 1/6 x Weight of an object on the Earth
Also,
Weight = Mass x Acceleration
Acceleration due to gravity, g = 9.8 m/s²
Therefore, weight of a 10 kg object on the Earth = 10 x 9.8 = 98 N
And, weight of the same object on the moon= 1.6 x 9.8 = 16.3 N.

A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate
(i) the maximum height to which it rises.
(ii) the total time it takes to return to the surface of the earth.

Answer :



According to the equation of motion under gravity:

v² - u²= 2 gs

Where,

u= Initial velocity of the ball

v= Final velocity of the ball

s= Height achieved by the ball

g= Acceleration due to gravity

At maximum height, final velocity of the ball is zero, i.e., v= 0

u = 49 m/s

During upward motion, g = - 9.8 m s^{- 2}

Let h be the maximum height attained by the ball.

Hence,



Let t be the time taken by the ball to reach the height 122.5 m, then according to the equation of motion:

v= u + gt

We get,



But,

Time of ascent = Time of descent

Therefore, total time taken by the ball to return = 5 + 5 = 10 s

(i) 122.5 m (ii) 10 s