Chapter 10 Gravitation Solutions
Question - 11 : - You have a bag of cotton and an iron bar, each indicating a mass of 100 kg when measured on a weighing machine. In reality, one is heavier than other. Can you say which one is heavier and why?
Answer - 11 : -
The bag of cotton is heavier than the iron bar. This is because the surface area of the cotton bag is larger than the iron bar. Hence, more buoyant force acts on the bag than that on an iron bar. This makes the cotton bag heavier than its actual value. For this reason, the iron bar and the bag of cotton show the same mass on the weighing machine, but actually the mass of cotton bag is more that that of the iron bar.
Actual weight = Measured Weight + Buoyant Force
Question - 12 : - How does the force of gravitation between two objects change when the distance between them is reduced to half?
Answer - 12 : - According to the universal law of gravitation, gravitational force (F) acting between two objects is inversely proportional to the square of the distance (r) between them, i.e.,
If distance r becomes r/2, then the gravitational force will be proportional to
Hence, if the distance is reduced to half, then the gravitational force becomes four times larger than the previous value.
Question - 13 : - Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?
Answer - 13 : - All objects fall on ground with constant acceleration, called acceleration due to gravity (in the absence of air resistances). It is constant and does not depend upon the mass of an object. Hence, heavy objects do not fall faster than light objects.
Question - 14 : - What is the magnitude of the gravitationalforce between the earth and a 1 kg object on its surface? (Mass of the earth is6 × 1024 kg and radius of the earth is 6.4 × 106 m).
Answer - 14 : -
According to the universal law ofgravitation, gravitational force exerted on an object of mass m isgiven by:
Where,
Mass of Earth, M = 6 × 1024 kg
Mass of object, m = 1 kg
Universal gravitational constant, G = 6.7 ×10−11 Nm2 kg−2
Since the object is on the surface of theEarth, r = radius of the Earth (R)
r = R = 6.4 × 106 m
Gravitationalforce, 
Question - 15 : - The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?
Answer - 15 : - According to the universal law of gravitation, two objects attract each other with equal force, but in opposite directions. The Earth attracts the moon with an equal force with which the moon attracts the earth.
Question - 16 : - If the moon attracts the earth, why does the earth not move towards the moon?
Answer - 16 : - The Earth and the moon experience equal gravitational forces from each other. However, the mass of the Earth is much larger than the mass of the moon. Hence, it accelerates at a rate lesser than the acceleration rate of the moon towards the Earth. For this reason, the Earth does not move towards the moon.
Question - 17 : - 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 - 17 : -
(i) Doubled (ii) One-fourth and one-ninth (iii) four times
According to the universal law of gravitation, the force of gravitation between two objects is given by:
(i) F is directly proportional to the masses of the objects. If the mass of one object is doubled, then the gravitational force will also get doubled.
(ii) F is inversely proportional to the square of the distances between the objects. If the distance is doubled, then the gravitational force becomes one-fourth of its original value.
Similarly, if the distance is tripled, then the gravitational force becomes one-ninth of its original value.
(iii) F is directly proportional to the product of masses of the objects. If the masses of both the objects are doubled, then the gravitational force becomes four times the original value.
Question - 18 : - What is the importance of universal law of gravitation?
Answer - 18 : - The universal law of gravitation proves that every object in the universe attracts every other object.
Question - 19 : - What is the acceleration of free fall?
Answer - 19 : -
Whenobjects fall towards the Earth under the effect of gravitational force alone,then they are said to be in free fall. Acceleration of free fall is 9.8 m s−2, which is constant forall objects (irrespective of their masses).
Question - 20 : - What do we call the gravitational force between the Earth and an object?
Answer - 20 : - Gravitational force between the earth and an object is known as the weight of the object.