In-text Questions and Answers
- State the universal law of gravitation.
- Answer: The universal law of gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
- Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.
- Answer: The formula to find the magnitude of the gravitational force (F) between the earth and an object on its surface is:
F = (G × M × m) / R²
where:
- F is the gravitational force,
- G is the universal gravitational constant,
- M is the mass of the earth,
- m is the mass of the object, and
- R is the radius of the earth.
- What do you mean by free fall?
- Answer: Free fall refers to the motion of an object where the only force acting on it is the gravitational force of the earth. In free fall, objects accelerate towards the earth due to gravity alone, without any resistance from air or other forces.
- What do you mean by acceleration due to gravity?
- Answer: Acceleration due to gravity is the acceleration experienced by an object when it is in free fall under the influence of the earth’s gravitational force. It is denoted by “g” and has a standard value of approximately 9.8 m/s² near the earth’s surface.
- What are the differences between the mass of an object and its weight?
- Answer:
- Mass is the amount of matter in an object and is measured in kilograms (kg). It is a scalar quantity and remains constant regardless of location.
- Weight is the force with which an object is attracted towards the earth due to gravity. It is a vector quantity and is measured in newtons (N). Weight depends on both the mass of the object and the acceleration due to gravity, and it varies with location.
- Answer:
- Why is the weight of an object on the moon 1/6th its weight on the earth?
- Answer: The weight of an object on the moon is 1/6th of its weight on the earth because the gravitational force on the moon is weaker than on the earth. This is because the moon’s mass is much smaller than the earth’s mass, leading to a lower gravitational pull on objects.
- Why is it difficult to hold a school bag having a strap made of a thin and strong string?
- Answer: It is difficult to hold a school bag with a thin strap because the thin strap exerts more pressure on a smaller area of the shoulder. This higher pressure makes it uncomfortable and painful to carry the bag for a long time.
- What do you mean by buoyancy?
- Answer: Buoyancy is the upward force exerted by a fluid on an object placed in it. This force opposes the weight of the object and can make the object float or appear lighter when submerged in the fluid.
- Why does an object float or sink when placed on the surface of water?
- Answer: An object floats on water if its density is less than the density of water, as the buoyant force is greater than the object’s weight. Conversely, an object sinks if its density is greater than water’s, as the weight of the object is greater than the buoyant force.
- You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg?
- Answer: The mass shown by the weighing machine is your actual mass. So, your mass is 42 kg, and it doesn’t change regardless of the location.
- 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 the other. Can you say which one is heavier and why?
- Answer: The iron bar is actually heavier than the bag of cotton. The weighing machine shows the same mass because it measures weight, which is mass plus the buoyant force of the air. The bag of cotton displaces more air due to its larger volume, experiencing a greater buoyant force, making it appear to have the same mass as the iron bar.
Exercise Questions and Answers
- How does the force of gravitation between two objects change when the distance between them is reduced to half?
- Answer: The gravitational force between two objects increases by four times when the distance between them is reduced to half. This is because gravitational force is inversely proportional to the square of the distance between the objects.
- Gravitational force acts on all objects in proportion to their masses. Why then, does a heavy object not fall faster than a light object?
- Answer: A heavy object does not fall faster than a light object because the acceleration due to gravity (g) is the same for all objects, regardless of their masses. Hence, both heavy and light objects fall at the same rate when only gravity acts on them.
- What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is 6 × 10²⁴ kg and radius of the earth is 6.4 × 10⁶ m.)
- Answer: The gravitational force (F) can be calculated using the formula:
F = (G × M × m) / R²
Substituting the values:
F = (6.7 × 10⁻¹¹ × 6 × 10²⁴ × 1) / (6.4 × 10⁶)²
F = 9.8 N
So, the gravitational force is 9.8 N.
- 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, smaller, or the same as the force with which the moon attracts the earth? Why?
- Answer: The earth attracts the moon with the same force with which the moon attracts the earth. According to Newton’s third law of motion, every action has an equal and opposite reaction. So, the force is equal in magnitude but acts in opposite directions.
- If the moon attracts the earth, why does the earth not move towards the moon?
- Answer: The earth does move towards the moon, but the movement is extremely small and not noticeable because the earth’s mass is much larger than the moon’s. According to Newton’s second law of motion, acceleration is inversely proportional to mass. The larger mass of the earth results in a very small acceleration.
- What happens to the force between two objects if:
- (i) The mass of one object is doubled?
- Answer: If the mass of one object is doubled, the gravitational force between the two objects also doubles.
- (ii) The distance between the objects is doubled and tripled?
- Answer: If the distance between the objects is doubled, the gravitational force becomes one-fourth. If the distance is tripled, the gravitational force becomes one-ninth.
- (iii) The masses of both objects are doubled?
- Answer: If the masses of both objects are doubled, the gravitational force becomes four times greater.
- (i) The mass of one object is doubled?
- What is the importance of the universal law of gravitation?
- Answer: The universal law of gravitation is important because it explains the force that binds us to the earth, the motion of planets around the Sun, the motion of the moon around the earth, and the phenomena of tides due to the moon and the Sun.
- What is the acceleration of free fall?
- Answer: The acceleration of free fall is the acceleration experienced by an object when it falls towards the earth due to gravity. Its value is approximately 9.8 m/s².
- What do we call the gravitational force between the earth and an object?
- Answer: The gravitational force between the earth and an object is called weight.
- Amit buys a few grams of gold at the poles as per the instruction of one of his friends. He hands over the same when he meets him at the equator. Will the friend agree with the weight of gold bought? If not, why?
- Answer: The friend might not agree with the weight of gold because the value of gravitational acceleration (g) is slightly less at the equator compared to the poles. This means that the same mass of gold would weigh slightly less at the equator than at the poles.
- Why will a sheet of paper fall slower than one that is crumpled into a ball?
- Answer: A sheet of paper falls slower than a crumpled ball because the flat sheet experiences more air resistance due to its larger surface area, which slows down its fall.
- Gravitational force on the surface of the moon is only 1/6th as strong as gravitational force on the earth. What is the weight in newtons of a 10 kg object on the moon and on the earth?
- Answer:
- On earth: Weight = mass × gravitational acceleration = 10 kg × 9.8 m/s² = 98 N
- On the moon: Weight = (1/6) × 98 N = 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.
- Answer: Using the formula v² = u² – 2gs, where v = 0 (at maximum height), u = 49 m/s, and g = 9.8 m/s²: 0 = 49² – 2 × 9.8 × s s = 122.5 m So, the maximum height is 122.5 meters.
- (ii) The total time it takes to return to the surface of the earth.
- Answer: Time to rise (t) = u/g = 49/9.8 = 5 seconds. So, the total time to rise and fall = 2 × 5 = 10 seconds.
- (i) The maximum height to which it rises.
- A stone is released from the top of a tower of height 19.6 m. Calculate its final velocity just before touching the ground.
- Answer: Using the formula v² = u² + 2gs, where u = 0, g = 9.8 m/s², and s = 19.6 m: v² = 0 + 2 × 9.8 × 19.6 v = 19.6 m/s The final velocity is 19.6 m/s.
- A stone is thrown vertically upward with an initial velocity of 40 m/s. Taking g = 10 m/s², find:
- (i) The maximum height reached by the stone.
- Answer: Using the formula v² = u² – 2gs, where v = 0 (at maximum height), u = 40 m/s, and g = 10 m/s²: 0 = 40² – 2 × 10 × s s = 80 meters So, the maximum height is 80 meters.
- (ii) The net displacement and the total distance covered by the stone.
- Answer: The net displacement after returning to the initial point is 0 meters, and the total distance covered is twice the maximum height, which is 160 meters.
- (i) The maximum height reached by the stone.
- Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = 6 × 10²⁴ kg and the mass of the Sun = 2 × 10³⁰ kg. The average distance between the two is 1.5 × 10¹¹ m.
- Answer: Using the formula:
F = (G × M × m) / R²
where G = 6.7 × 10⁻¹¹ N m²/kg²,
F = (6.7 × 10⁻¹¹ × 6 × 10²⁴ × 2 × 10³⁰) / (1.5 × 10¹¹)²
F ≈ 3.57 × 10²² N
- A stone is allowed to fall from the top of a tower 100 m high, and at the same time, another stone is projected vertically upwards from the ground with a velocity of 25 m/s. Calculate when and where the two stones will meet.
- Answer: Let the two stones meet after time t seconds. For the stone falling from the top:
Distance covered by stone 1 = s₁ = 1/2 × g × t² = 1/2 × 10 × t² = 5t²
For the stone projected upwards:
Distance covered by stone 2 = s₂ = ut – 1/2 × g × t² = 25t – 5t²
Since the sum of the distances covered by both stones is equal to the height of the tower:
5t² + (25t – 5t²) = 100
25t = 100
t = 4 seconds
The stones will meet after 4 seconds.
Substituting t = 4 in s₁:
s₁ = 5 × 4² = 80 meters
So, they meet 80 meters below the top of the tower.
- A ball thrown up vertically returns to the thrower after 6 seconds. Find:
- (a) The velocity with which it was thrown up.
- Answer: Time to rise = 6/2 = 3 seconds. Using the formula u = g × t:
u = 10 × 3 = 30 m/s
- (b) The maximum height it reaches.
- Answer: Using the formula s = ut – 1/2 × g × t²:
s = 30 × 3 – 1/2 × 10 × 9 = 90 – 45 = 45 meters
- (c) Its position after 4 seconds.
- Answer: After 4 seconds, the ball would be on its way down. Distance covered in 4 seconds:
s = ut – 1/2 × g × t² = 30 × 4 – 1/2 × 10 × 16 = 120 – 80 = 40 meters above the ground.
- (a) The velocity with which it was thrown up.
- In what direction does the buoyant force on an object immersed in a liquid act?
- Answer: The buoyant force on an object immersed in a liquid acts in the upward direction.
- Why does a block of plastic released underwater come up to the surface of the water?
- Answer: A block of plastic comes up to the surface of the water because the buoyant force acting on it is greater than its weight, causing it to float.
- The volume of 50 g of a substance is 20 cm³. If the density of water is 1 g/cm³, will the substance float or sink?
- Answer: The density of the substance = mass/volume = 50 g/20 cm³ = 2.5 g/cm³. Since the density of the substance is greater than the density of water (1 g/cm³), it will sink.
- The volume of a 500 g sealed packet is 350 cm³. Will the packet float or sink in water if the density of water is 1 g/cm³? What will be the mass of the water displaced by this packet?
- Answer: The density of the packet = mass/volume = 500 g/350 cm³ ≈ 1.43 g/cm³. Since the density of the packet is greater than the density of water (1 g/cm³), it will sink.
- The mass of the water displaced by the packet = volume × density of water = 350 cm³ × 1 g/cm³ = 350 g.