Class 9 · Advanced ScienceNCERT 2026 Revised Syllabus
Chapter 4: The Geometry of Power - Advanced Simple Machines
Science Advanced
Mechanical advantage of machines, wheel and axle, gear trains, and tension in pulley systems (Atwood machine calculations).
Find complete NCERT solutions for Class 9 Advanced Science, Science Advanced Chapter 4. Every question has a clear, step-by-step answer.
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Activity 4.1 (Reflective Questions)(1 questions)
1
Is the truck driver extremely strong? Does the crane create extra force? Does the cyclist get ‘free’ speed?
Board Level Answers
Ans.
Solution:- No. In each case, a machine provides mechanical advantage.
- A smaller input force/effort produces a larger output force or motion.
- No extra energy is created.Answer: No; machines provide mechanical advantage without creating extra energy.
Wheel and Axle (Think and Answer)(1 questions)
1
Why is the steering wheel large and the steering column (axle) small? Why not make both of equal size?
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Ans.
Solution:- A larger wheel radius compared to the axle radius gives a greater mechanical advantage.
- A small effort applied on the wheel produces a much larger turning force at the axle.Answer: A larger wheel compared to the axle gives greater mechanical advantage and a larger turning force at the axle.
Quick Check (Gear Train)(2 questions)
1
Hard
If the seconds gear is 2 mm, and the seconds-to-minutes and minutes-to-hours gear ratios are both 60:1, how large would the hour gear be in metres?
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Ans.
Solution:- Minute gear
$= 2 \times 60 = 120 \text{ mm}$.
- Hour gear $= 120 \times 60 = 7200 \text{ mm} = 7.2 \text{ metres}$.Answer: The hour gear would be 7.2 metres.2
Which of the three hands’ gear should be directly connected to the motor? Why?
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Ans.
Solution:- The seconds-hand gear must rotate the fastest.
- It drives the slower minute and hour gears through the gear train.Answer: The seconds-hand gear should be connected directly to the motor.
Tension (Activity, Let Us Calculate)(4 questions)
1
Hard
For the 0.55 kg mass moving downward: state the downward force (weight).
Board Level Answers
Ans.
Solution:Weight
$= mg = 0.55 \times 9.8 = 5.39 \text{ N}$Answer: Downward force = 5.39 N.2
Hard
For the 0.5 kg mass moving upward: state the downward force (weight).
Board Level Answers
Ans.
Solution:Weight
$= mg = 0.5 \times 9.8 = 4.9 \text{ N}$Answer: Downward force = 4.9 N.3
Hard
Add both net-force equations (0.55g - T = 0.55a and T - 0.5g = 0.5a) to find the system’s acceleration.
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Ans.
Solution:
$0.55g - T = 0.55a$
$T - 0.5g = 0.5a$Adding: $0.55g - 0.5g = 0.55a + 0.5a$$0.05g = 1.05a$$a = \frac{0.05 \times 9.8}{1.05} \approx 0.47 \text{ m/s}^{2}$Answer: $a \approx 0.47 \text{ m/s}^{2}$.4
Hard
Find the tension in the string for this system.
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Ans.
Solution:
$T - 0.5g = 0.5a$$T = 0.5(g + a) = 0.5 \times (9.8 + 0.47) \approx 5.13 \text{ N}$Answer: Tension $\approx 5.13 \text{ N}$.Check Your Understanding (Tension)(5 questions)
1
Show the direction of weight and tension for both objects m1 and m2 in a pulley diagram.
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Ans.
Solution:- Tension in the rope acts upward on both
$m_1$ and $m_2$, toward the pulley.
- The weight ($mg$) of each mass acts vertically downward due to gravity.Answer: Tension acts upward toward the pulley; weight acts vertically downward on each mass.2
Hard
An 8 kg mass hangs freely from a single fixed pulley. The system is at rest. Find the tension in the rope.
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Ans.
Solution:Since the system is at rest,
$T = mg = 8 \times 9.8 = 78.4 \text{ N}$.Answer: Tension = 78.4 N.3
Hard
Observe a diagram with a 10 kg and a 20 kg mass connected over a pulley. In which direction will the rope move, and what is the net downward force?
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Ans.
Solution:- The heavier 20 kg mass moves downward; the 10 kg mass moves upward.
- Net force
$= (20 - 10) \times 9.8 = 10 \times 9.8 = 98 \text{ N}$.Answer: Rope moves toward the 20 kg side; net downward force = 98 N.4
Hard
A 6 kg mass hangs freely from a single fixed pulley. The system is at rest. Find the tension in the rope.
Board Level Answers
Ans.
Solution:Since the system is at rest,
$T = mg = 6 \times 9.8 = 58.8 \text{ N}$.Answer: Tension = 58.8 N.5
Hard
Two objects having masses 2 kg and 6 kg are connected over a frictionless pulley with the help of a rope. Find the acceleration and tension in the rope.
Board Level Answers
Ans.
Solution:
$a = \frac{(m_2 - m_1)g}{m_1 + m_2} = \frac{(6 - 2) \times 9.8}{8} = 4.9 \text{ m/s}^{2}$$T = m_1(g + a) = 2 \times (9.8 + 4.9) = 29.4 \text{ N}$Answer: Acceleration = 4.9 m/s²; tension = 29.4 N.