Case Study:

During a school trip to a hill station at an altitude of 2500 m, Riya noticed something unusual. When she stood on a digital weighing machine at home in the plains, her weight was recorded as 50 kg. However, at the hill station, the same machine showed her weight as 49.7 kg. Confused, she wondered if she had actually lost weight in just one day.

If you’ve ever wondered about the basics of why we stay grounded, check out our deep dive on why things fall due to gravity.

Her teacher explained that the change was not due to loss of mass but due to a variation in the value of acceleration due to gravity (g).

To master this concept, you might find our fun guide to free fall and acceleration helpful for visualizing the math.

According to NCERT concepts, the value of g decreases with an increase in altitude because the distance between the object and the center of the Earth increases. Since weight is the force exerted by gravity on an object, it depends on g.

The relationship is given by:

W = mg

This formula is a direct application of the Universal Law of Gravitation, which we’ve simplified with interactive problems for you.

Thus, even though Riya’s mass remained constant, the decrease in g at higher altitudes caused a slight reduction in her weight. This observation raised an important question: how does the variation of g affect weight measurements in different geographical locations?

CASE-BASED QUESTIONS

MCQs

Q1. The decrease in Riya’s weight at the hill station is mainly due to:
A. Decrease in her mass
B. Increase in altitude affecting g
C. Change in weighing machine
D. Loss of body fluids

Q2. Which of the following remains constant when a person moves from plains to a hill station?
A. Weight
B. Mass
C. Gravitational force
D. Acceleration due to gravity

Assertion - Reason

Q3. Assertion (A): The value of acceleration due to gravity decreases with altitude.
Reason (R): The distance between the object and the Earth’s center increases with altitude.

A. Both A and R are true, and R is the correct explanation of A
B. Both A and R are true, but R is not the correct explanation
C. A is true, but R is false
D. A is false, but R is true

Application-Based Questions

Q4. If another student has a mass of 60 kg, how will their weight change at the hill station compared to the plains? Explain briefly.

Q5. Why do weighing machines give slightly different readings at different altitudes even if calibrated properly?

Data / Logic-Based Question

Q6. A person’s weight is 600 N at sea level where g = 9.8 m/s². At a hill station, g reduces to 9.75 m/s². Calculate the new weight of the person.

ANSWER KEY WITH EXPLANATION

A1. B - Increase in altitude affecting g
Explanation: Weight depends on g. At higher altitude, g decreases, reducing weight.

A2. B - Mass
Explanation: Mass is constant irrespective of location; weight varies with g.

Q3. A - Both A and R are true, and R is the correct explanation of A
Explanation: As altitude increases, distance from Earth’s center increases, reducing gravitational force and g.

A4. The student’s weight will decrease slightly.
Explanation: Since weight = mg, a decrease in g leads to a decrease in weight while mass remains unchanged.

A5. Because g varies with altitude.
Explanation: Weighing machines measure weight (force), which depends on gravitational acceleration.

A6. Mass = 600 / 9.8 ≈ 61.22 kg
New weight = 61.22 × 9.75 ≈ 597.4 N
Explanation: Lower g results in reduced weight.

Ready to ace your exams? Test your knowledge with our Class 9 Physics worksheets, or challenge yourself with unsolved practice papers. If you get stuck, you can always refer to our solved practice papers for step-by-step guidance.

HOTS EXTENSION QUESTIONS

Q1. If Earth’s radius suddenly increased while mass remained constant, how would it affect g and human weight? Explain.

Q2. Why would astronauts experience near weightlessness even though Earth’s gravity still acts on them?

Curious about the physics of orbit? Explore the truth behind whether astronauts actually float in space and the reality of weightlessness.