Case Based Questions: Gravitation | Science Class 9 PDF Download

Q1: Read the following passage and answer the questions that follow:

i. State the formula for the Universal Law of Gravitation. (1 mark)
ii. How does the force between two objects change if the distance between them is doubled? (2 mark)
iii. Why do we not notice the gravitational attraction between small objects like two chairs placed next to each other? (1 mark)

Ans:
i. The formula for the Universal Law of Gravitation is.
F = (G x M x m) / d²
where F is the gravitational force, G is the universal gravitational constant, M and m are the masses of the objects, and d is the distance between them.
ii. If the distance d is doubled, the force becomes:
F' = (G × M × m) / (2d)² = F / 4
iii. This means the gravitational force reduces to one-fourth of its original value.
We do not notice the gravitational attraction between small objects because their masses are very small compared to celestial bodies like Earth and the Sun. The force is too weak to be observed.

Q2: Read the following passage and answer the questions that follow:

i. What is the value of acceleration due to gravity on Earth? (1 mark)
ii. Why do objects with different masses fall at the same rate during free fall? (2 mark)
iii. Why does a sheet of paper fall slower than a stone when dropped from the same height? (1 mark)

Ans:
i. The acceleration due to gravity on Earth is 9.8 m/s².
ii. According to Newton’s Second Law, the force acting on an object is F = mg. Since acceleration a = F/m, the mass cancels out, leaving a = g. This means all objects fall at the same rate in the absence of air resistance.
iii. A sheet of paper falls slower than a stone because of air resistance, which opposes its motion. If dropped in a vacuum, both would fall at the same rate.

Q3: Read the following passage and answer the questions that follow:

i. What is the formula to calculate weight? (1 mark)
ii. If an object weighs 60 N on Earth, how much will it weigh on the Moon? (2 mark)
iii. Why do astronauts on the Moon appear to move in slow motion? (1 mark)

Ans:
i. The formula for weight is W = mg, where m is the mass of the object and g is the acceleration due to gravity.
ii. The weight of the object on the Moon is
W_m = W_e / 6 = 60 / 6 = 10N
So, the object weighs 10 N on the Moon.
iii. Astronauts appear to move in slow motion on the Moon because the gravity is weaker (1/6th of Earth's gravity), resulting in lower weight and reduced force of movement.

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Q4: Read the following passage and answer the questions that follow:

i. What is buoyant force? (1 mark)
ii. Why does a heavy iron ship float while a small iron nail sinks? (2 mark)
iii. Why is it easier to lift a heavy object underwater than in air? (1 mark)

Ans:
i. Buoyant force is the upward force exerted by a fluid on an object immersed in it.
ii. An iron nail sinks because its density is higher than that of water, and the buoyant force is less than its weight. However, a ship is designed with a hollow structure to displace more water, increasing the buoyant force, which makes it float.
iii. Underwater, an object experiences an upward buoyant force, which reduces the net weight of the object, making it easier to lift.

Q5: Read the following passage and answer the questions that follow:

i. State Archimedes' Principle. (1 mark)
ii. How does Archimedes' Principle explain why some objects sink while others float? (2 mark)
iii. How does a submarine control its depth using this principle? (1 mark)

Ans:
i. Archimedes' Principle states that a body immersed in a fluid experiences an upward force equal to the weight of the displaced fluid.
ii. An object sinks if its weight is greater than the buoyant force acting on it. It floats if its weight is less than or equal to the buoyant force.
iii. A submarine controls its depth by adjusting the water level in its ballast tanks.
To descend, it fills the tanks with water, increasing its weight.
To ascend, it pumps out water, reducing its weight and increasing buoyant force.

Q6: Read the following passage and answer the questions that follow:

i. What happens to the force of gravity as we move higher above the Earth’s surface? (1 mark)
ii. Why is the value of g greater at the poles than at the equator? (2 mark)
iii. Why do astronauts feel weightless in space? (1 mark)

Ans:
i. The force of gravity decreases as we move higher above the Earth's surface because it is inversely proportional to the square of the distance from the Earth's center.
ii. The Earth is not a perfect sphere; it is slightly flattened at the poles and bulged at the equator. This makes the radius at the equator greater than at the poles. Since g = GM/R², a larger radius at the equator results in a smaller value of g compared to the poles.
iii. Astronauts feel weightless in space because they are in a state of free fall around the Earth. Even though gravity is still acting on them, they are continuously falling along with the spacecraft, creating the sensation of weightlessness.

Q7: Read the following passage and answer the questions that follow:

i. Define pressure and its SI unit. (1 mark)
ii. Why is it easier to cut vegetables with a sharp knife than with a blunt one? (2 mark)
iii. Why do heavy trucks have broad tires? (1 mark)

Ans:
i. Pressure is the force per unit area and is given by:
P =Thrust / Area
The SI unit of pressure is Pascal (Pa) or N/m².
ii. A sharp knife has a smaller surface area, which increases the pressure applied for the same force, making it easier to cut. A blunt knife has a larger area, reducing the pressure and making cutting difficult.
iii. Heavy trucks have broad tires to distribute their weight over a larger surface area, reducing pressure on the road and preventing sinking.

Q8: Read the following passage and answer the questions that follow:

i. What is the final velocity of the ball at its highest point? (1 mark)
ii. Calculate the maximum height reached by the ball. (2 mark)
iii. Why does the time taken to go up equal the time taken to come down? (1 mark)

Ans:
i. The final velocity at the highest point is 0 m/s because the ball momentarily stops before falling back.
ii. Using the equation v² = u² - 2gh:
Initial velocity, u = 20 m/s
Final velocity, v = 0 m/s
Acceleration due to gravity, g = 9.8 m/s²
0 = (20)² - 2(9.8)h
400 = 19.6 h
h = 20.4 m
So, the maximum height reached is 20.4 m.
iii. The time taken to go up equals the time taken to come down because motion under gravity is symmetrical. Since acceleration is constant, the ball loses velocity at the same rate while going up as it gains while coming down.

Q9: Read the following passage and answer the questions that follow:

i. Define density and give its SI unit. (1 mark)
ii. Why does a wooden block float while an iron block of the same size sinks? (2 mark)
iii. Why does a ship made of iron float while a small iron ball sinks? (1 mark)

Ans:
i. Density is the mass per unit volume and is given by:
p = m/V
The SI unit of density is kg/m³.
ii. A wooden block floats because its density is lower than water, meaning the buoyant force is greater than its weight. An iron block sinks because its density is higher than water, making the buoyant force less than its weight.
iii. A ship is hollow, allowing it to displace more water, increasing the buoyant force, which makes it float. A solid iron ball displaces very little water, so the buoyant force is not enough to counteract its weight, making it sink.

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Q10: Read the following passage and answer the questions that follow:

i. What does Archimedes' Principle state? (1 mark)
ii. How does a submarine rise and sink in water? (2 mark)
iii. Why does a person feel lighter while swimming in water? (1 mark)

Ans:
i. Archimedes' Principle states that a body immersed in a fluid experiences an upward force equal to the weight of the displaced fluid.
ii. A submarine has ballast tanks that control its depth:
To sink, it fills the tanks with water, increasing weight.
To rise, it pumps out water and fills the tanks with air, reducing weight and increasing buoyant force.
iii. A person feels lighter in water because of buoyant force, which partially supports their weight, reducing the force they feel.

Q11: Read the following passage and answer the questions that follow:

i. What force is responsible for the falling motion of both the hammer and the feather? (1 mark)
ii. If the acceleration due to gravity on the Moon is 1.63 m/s², calculate the time taken by the feather to fall from a height of 5 meters. (2 mark)
iii. Why do objects fall at the same rate on the Moon, whereas on Earth, a feather falls slower than a hammer? (1 mark)

Ans:
i. Gravitational force.
ii. Given:
Initial velocity, u = 0
Acceleration due to gravity on the Moon, g = 1.63 m/s²
Distance, s = 5 m
Using s = ut + (1/2)gt²
5 = 0 + 1/2(1.63)t²
5 = 0.815t²
t² = 5/0.815 = 6.13
t = 2.47 s
iii. On Earth, air resistance slows down the feather more than the hammer. In a vacuum (like on the Moon), there is no air resistance, so both objects fall at the same rate.

Q12: Read the following passage and answer the questions that follow:

i. What happens to the velocity of the football when it reaches its highest point? (1 mark)
ii. If the football is kicked upwards with an initial velocity of 20 m/s, calculate the maximum height it reaches. (Take g = 9.8 m/s².) 
(2 mark)
iii. Why does the ball stop momentarily at the highest point before coming down? (1 mark)

Ans:
i. The velocity becomes zero at the highest point.
ii. Using v² = u² + 2as:
0 = 20² + 2(-9.8)s
400 = 19.6s
s = 20.41 m
iii. At the highest point, all the initial kinetic energy is converted into gravitational potential energy, momentarily stopping the ball before gravity pulls it back down.

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Q13: Read the following passage and answer the questions that follow:

i. What is the relation between weight and acceleration due to gravity? (1 mark)
ii. Calculate the astronaut’s weight on the Moon. (2 mark)
iii. Why does the astronaut’s mass remain the same on the Moon but not her weight? (1 mark)

Ans:
i. Weight is given by W = mg, meaning it depends on both mass and gravity.
ii. Given:
Weight on Earth, W_e = 600 N
Weight on Moon, W_m = (1/6) W_e
W_m = 600/6 = 100 N
iii. Mass is an intrinsic property and does not change with location, whereas weight depends on gravitational pull, which varies from planet to planet.

Q14: Read the following passage and answer the questions that follow:

i. What is the acceleration acting on the car during its fall? (1 mark)
ii. Calculate the height of the bridge. (Take g = 9.8 m/s².) (2 mark)
iii. Would the time of fall change if the car was heavier? Explain.(1 mark)

Ans:
i. Acceleration due to gravity, g = 9.8 m/s².
ii. Using s = ut + (1/2) gt²:
s = 0 + (1/2)(9.8)(3)²
s = 44.1 m
iii. No, the time of fall depends only on gravity and height, not on mass.

Q15: Read the following passage and answer the questions that follow:

i. What force increases as the submarine sinks? (1 mark)
ii. If the pressure at 10 m depth is 100,000 Pa, calculate the pressure at 50 m depth, assuming it increases linearly. (2 mark)
iii. Why do deep-sea creatures have thick, strong bodies? (1 mark)

Ans:
i. Hydrostatic pressure.
ii. Given:
P₅₀ = P₁₀ × (50/10)
P₅₀ = 100,000 × 5 = 500,000 Pa
iii. They need thick bodies to withstand the enormous pressure at great depths.