CHAPTER 10: Gravitation (Date : 21-10-2022)

Question 1:

Consider the following statements regarding the Free Fall on the earth:

Free-falling objects encounter air resistance.
Acceleration experienced by an object is dependent on its mass.

Which of the statements given above is/are correct?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Correct Answer : D

Explanation

A free-falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. There are a few important motion characteristics that are true of free-falling objects:
- Free-falling objects do not encounter air resistance (although in realty air resistance is present on the earth). Hence, statement 1 is not correct.
- All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for back-of-the-envelope calculations)
- Object experiences acceleration during free fall and this acceleration experienced by an object is independent of its mass. This means that all objects hollow or solid, big or small, should fall at the same rate. Hence, statement 2 is not correct.
According to a story, Galileo dropped different objects from the top of the Leaning Tower of Pisa in Italy to prove the same.

Question 2:

Consider the following statements:

The force that binds us to the earth;
The motion of the moon around the earth;
The motion of planets around the Sun; and
The tides are due to the moon and the Sun.

Which of the above-mentioned phenomena can be explained by the universal law of gravitation?

1 only
1 and 2 only
1, 2 and 3 only
1, 2, 3 and 4

Correct Answer : D

Explanation

UNIVERSAL LAW OF GRAVITATION:

Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them. The force is along the line joining the centres of two objects.
According to the universal law of gravitation, the force between two objects is directly proportional to the product of their masses. That is,
- F∝M x m
And the force between two objects is inversely proportional to the square of the distance between them, i.e., F ∝ (1/d2).
- G = (Fd2/M x m) and G = 6.673 × 10–11 N m2 kg–2.
The law is universal in the sense that it is applicable to all bodies, whether the bodies are big or small, whether they are celestial or terrestrial.
IMPORTANCE OF THE UNIVERSAL LAW OF GRAVITATION: The universal law of gravitation successfully explained several phenomena which were believed to be unconnected:
- the force that binds us to the earth;
- the motion of the moon around the earth;
- the motion of planets around the Sun; and
- the tides due to the moon and the Sun.
Hence, option D is correct.

Question 3:

Consider the following statements regarding the Mass and weight:

The mass of an object is constant and does not change from place to place.
Weight of an object is the force with which it is attracted towards the earth.
Weight has both magnitude and direction but mass has only magnitude.

Which of the statements given above is/are correct?

1 only
1, and 2 only
1, 2 and 3
None of the Above

Correct Answer : C

Explanation

MASS:
- The mass of an object is the measure of its inertia. The greater the mass, the greater the inertia is. It remains the same whether the object is on the earth, the moon or even in outer space.
- Thus, the mass of an object is constant and does not change from place to place. Hence, statement 1 is correct.
WEIGHT:
- The earth attracts every object with a certain force and this force depends on the mass (m) of the object and the acceleration due to gravity (g).
- The weight of an object is the force with which it is attracted towards the earth. Hence, statement 2 is correct.
- The force of attraction of the earth on an object is known as the weight of the object.
  The weight of an object is the force with which it is attracted towards the earth. The weight is a force acting vertically downwards, it has both magnitude and direction but Mass has only magnitude. Hence, statement 3 is correct.
  The mass of an object remains the same everywhere, that is, on the earth and on any planet whereas its weight depends on its location because g depends on location.
- Due to this the moon exerts lesser force of attraction on objects.
  - Weight of the object on the moon = (1/6) × its weight on the earth.

Question 4:

Consider the following statements regarding thrust and pressure:

The net force in a perpendicular direction is called thrust and the force per unit area is known as pressure.
Both have the same units.

Which of the statements given above is/are correct?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Correct Answer : A

Explanation

Thrust and Pressure:

The net force in a particular direction (thrust) and the force per unit area (pressure) acting on the object.
Weight is the force acting vertically downwards.
The force acting on an object perpendicular to the surface is called thrust. The SI unit of thrust is newton (N). Hence, statement 1 is correct.
- Thrust does not depend on the area of the surface.
The effects of forces of the same magnitude on different areas are different. Therefore, the effect of thrust depends on the area on which it acts.
The thrust on unit area is called pressure. Pressure= Thrust/area
- Pressure is the force acting per unit area on an object.
- The SI unit of pressure is newton per square meter Nm–2. Hence, statement 2 is not correct.
- Pressure depends on the area of the surface on which it acts.
The same force acting on a smaller area exerts a larger pressure, and a smaller pressure on a larger area.

Question 5:

Consider the following statements:

The magnitude of force of buoyancy depends on fluid’s density.
The unit of relative density is the same as the unit of density.

Which of the statements given above is/are not correct?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Correct Answer : B

Explanation

BUOYANCY:
- Buoyancy is the tendency of an object to float in a fluid. All liquids and gases in the presence of gravity exert an upward force known as the buoyant force on any object immersed in them.
- All objects experience a force of buoyancy when they are immersed in a fluid. The magnitude of this buoyant force depends on the density of the fluid. Hence, statement 1 is correct.
Relative Density:
- The density of a substance is defined as the mass of a unit volume. The unit of density is kilogram per metre cube (kg m–3).
- The density of a given substance, under specified conditions, remains the same.
- The density of a given sample of a substance can help us to determine its purity. It is often convenient to express density of a substance in comparison with that of water.
- The relative density of a substance is the ratio of its density to that of water:
  - Relative density = Density of the Substance/Density of water
  - Since the relative density is a ratio of similar quantities, it has no unit. Hence, statement 2 is not correct.

Question 6:

Consider the following statements regarding Kepler’s Laws of planetary motion:

The orbit of the planets is an elliptical shape.
Newton used the third law of Kepler to calculate the gravitational force of attraction.

Which of the statements given above is/are correct?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Correct Answer : C

Explanation

Johannes Kepler derived three laws, which govern the motion of planets. These are called Kepler’s laws. These are:
- The orbit of a planet is an ellipse with the Sun at one of the foci. Hence, statement 1 is correct.
- The line joining the planet and the Sun sweeps equal areas in equal intervals of time.
- The cube of the mean distance of a planet from the Sun is proportional to the square of its orbital period T. Or, r3/T2 = constant.
It is important to note that Kepler could not give a theory to explain the motion of planets. It was Newton who showed that the cause of the planetary motion is the gravitational force that the Sun exerts on them. Newton used the third law of Kepler to calculate the gravitational force of attraction. The gravitational force of the earth is weakened by distance. Hence, statement 2 is correct.