The Geometry of Power Advanced Simple Machines Class 9 Question Answer Advanced Science Chapter 4

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The Geometry of Power Advanced Simple Machines Class 9 Questions and Answers

The Geometry of Power Advanced Simple Machines Question Answer Class 9

Quick Check

Question 1.
In a mechanical watch, a single power source (a spring or motor) must move three different hands at three different speeds. This is achieved through a gear train, where the ‘output’ of one gear becomes the ‘input’ for the next. The seconds-to-minutes gear ratio is 60 : 1 and the minutes to hours ratio is 60 :1.
(i) If the seconds gear is 2 mm, how large would the hour gear be in meters?
(ii) Which of the three hands gear should be directly connected to the motor? Why?
Answer:
(i) Seconds to minutes ratio = 60 : 1
Minutes to hours ratio = 60 : 1
Overall ratio (second to hours) = 60 × 60 = 3600 : 1
Hour gear diameter = 2 mm × 3600
= 7200 mm = 7.2 m

(ii) the second hand moves the fastest (1 full rotation every 60 seconds). The motor or spring also rotate at high speed. Connecting the fastest gear directly to the motor allows the gear train to gradually reduce the speed for slower minutes and hours hands. If the slow hour gear were directly, it would not match the high speed of the motor.

Check Your Understanding

Question 1
Show the direction of weight and tension for both objects m₁ and m₂.

Answer:

Question 2.
An 8 kg mass hangs freely from a single fixed pulley. The system is at rest. Find the tension in the rope.
Answer:
Since the system is at rest, the rope just has to hold up the weight of the mass. The tension is equal to the weight.
Mass (m) = 8 kg
Gravity (g) = 9.8 m/s²
Weight (w) = 8 × 9.8 = 78.4 N
Tension is exactly the same as the weight T = 78.4 N.

Question 3.
Observe the given diagram. Find out in which direction the rope will move? What will be the net downward force?

Answer:

The rope will move toward the heavier side because the 20 kg mass is heavier than the 10 kg mass. Therefore, the 20 kg mass will move downward and 10 kg mass will move upward.
Net Downward Force
The net force (F_net) is the difference between the two weights pulling in opposite directions.
W = m × g
So, right weight (w₁) = 20 × 9.8 = 196 N
Left weight (W₂) = 10 × 9.8 = 98 N
F_net = 196 N – 98 N = 98 N
The net downward force acting on the system is 98 N (acting in the direction of the 20 kg mass).

Question 4.
A 6 kg mass hangs freely from a single fixed pulley. The system is at rest. Find the tension in the rope
Answer:
Since the system is at rest, the tension in the rope must exactly balance the weight of the hanging mass to keep it from moving.
Mass (m) = 6 kg
Gravity (g) = 9.8 m / s²
The weight (w) of the object is the downward force and the tension (T) is the upward force.
Because there is no motion,
T = w
w = mg
= 6 × 9.8
w = 58.8 N

Question 5.
Two objects having masses 2 kg and 6 kg are connected over a frictionless pulley with the help of rope. Find acceleration and tension in the rope.
Answer:
To find the acceleration and tension, we treat the two masses as a single system.
Because the 6 kg mass is heavier, it will accelerate downward, pulling the 2 kg mass upward.

The acceleration of the system is the net force divided by the total mass.
a = \(\frac{\left(m_2-m_1\right) g}{\left(m_1+m_2\right)}\)
⇒ a = \(\frac{(6-2) \times 9.8}{6+2}\)
= \(\frac{39.2 N}{8 kg}\)
= 4.9 m/s²
Tension,
T = m₁ (g + a)
= 2 × (9.8 + 4.9)
= 2 × 14.7 = 29.4 N

The Geometry of Power Advanced Simple Machines Class 9 MCQ

Question 1.
In a wheel and axle system, why is the steering wheel typically much larger than the steering column (axle) it is attached to?
(A) To reduce the friction between the wheel and the axle.
(B) To multiply the input force applied by the driver.
(C) To ensure both the wheel and axle rotate at different speeds.
(D) To increase the speed at which the axle rotates.
Answer:
(B) To multiply the input force applied by the driver.
According to the formula
MA = \(\frac{\text { Radius of wheel }}{\text { Radius of axle }}\)
a larger wheel radius creates a higher mechanical advantage to multiply force.

Question 2.
A machine has a calculated ideal mechanical advantage of 10. If the machine is used in a real-world scenario with friction, what can be said about its efficiency (η)?
(A) The efficiency will be less than 100%.
(B) The efficiency will be greater than 100%.
(C) The efficiency will be exactly 100%.
(D) The efficiency is not affected by friction.
Answer:
(A) The efficiency will be less than 100%.
Real machines always lose some input work to friction, meaning the useful output work is always less than the total input work.

Question 3.
What happens to the tension in a thread when an object hanging from it is replaced by a heavier object?
(A) The tension increases.
(B) The tension stays the same because it is the same thread.
(C) The tension becomes zero because of the extra weight.
(D) The tension decreases because the thread stretches.
Answer:
(A) The tension increases.
Tension is the pulling force that travels through the string, as the downward weight (load) increases, the upward pulling force (tension) must also increase.

Question 4.
A 5 kg mass is suspended stationary from a rope. If the acceleration due to gravity (g) is 9.8 m/s2 what is the tension in the rope?
(A) 9.8 N
(B) 49 N
(C) 5 N
(D) 0 N
Answer:
(B) 49 N
In a stationary state (equilibrium), tension (T) equals weight (mg),
so 5 kg × 9.8 m/s² = 49 N

Question 5.
A truck’s steering wheel has a radius of 30 cm and the axle has a radius of 3 cm. If the driver applies 100 N of effort to the wheel, what is the maximum resistance force they can overcome at the axle in an ideal system?
(A) 1000 N
(B) 100 N
(C) 10 N
(D) 300 N
Answer:
(A) 1000 N
The mechanical advantage is \(\frac{30}{3}\) = 10.
Since, Load = Effort × MA, the result is 100 N × 10 = 1000 N

Assertion-Reason Questions

Directions (Q. Nos. 1 – 3): In each of the following questions, a statement of Assertion is given by the corresponding statement of Reason. Of the statements, mark the correct answer as.
(A) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
(B) Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion.
(C) Assertion is true, but Reason is false.
(D) Assertion is false, but Reason is true.

Question 1.
Assertion (A): A truck driver can turn a massive vehicle using only two hands.
Reason (R): The large radius of the steering wheel compared to the small radius of the steering column creates a mechanical advantage that multiplies the driver’s input force.
Answer:
(A) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
The geometry of the wheel and axle allows a small effort to overcome a large resistance.

Question 2.
Assertion (A): In a mechanical watch, the hour hand gear is geometrically much larger than the seconds hand gear
Reason (R): A gear train is used to ensure that all hands of the watch move at the exact same rotational acceleration.
Answer:
(C) Assertion is true, but Reason is false.

While the Assertion is true (the gears must be larger to accommodate the 60 : 1 ratios), the Reason is false, the gears are specifically designed to move the hands at different speeds.

Question 3.
Assertion (A): If you replace a light bob with a heavier bob on a thread, the tension inside the thread increases.
Reason (R): Tension is a pulling force that acts along the length of the string and pulls away from the object attached to it.
Answer:
(B) Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion.

Both statements are true. However, the Reason defines what tension is, but it doesn’t directly explain why it increases (which is because the downward weight force has increased, requiring a larger upward reaction force to maintain equilibrium).

The Geometry of Power Advanced Simple Machines Class 9 Extra Questions and Answers

Case/Source Based Questions

Directions (Q. No. 1): Answer the questions on the basis of your understanding of the following passage and related studied concepts.

Question 1.
To understand tension, a simple activity is performed. A thread is hung from an iron stand and its natural length is observed. When a small bob is attached to the lower end, the thread stretches slightly. When the small bob is replaced with a heavier bob, the thread stretches more. This shows that a greater pulling force acts on the thread as the attached weight increases. Next, the thread is passed over a pulley and equal weights are placed on both sides. The system remains at rest because the forces are balanced. However, when one side has a heavier weight, the system moves toward the heavier side.

i. What is tension? How is it produced in a thread?
ii. Why does the thread stretch more when a heavier bob is attached?
iii. What happens when equal weights are placed on both sides of the pulley? Why does the system remain at rest?
iv. If one side of the pulley has a heavier weight, in which direction does the system move? Explain why.
Answer:
i. Tension is the internal pulling or stretching force that develops in a stretched string, thread, rope or cable.
It is produced when an object is hung from the thread. The weight of the object pulls the thread downward, and the thread pulls the object upward with an equal force. This mutual pulling force inside the thread is called tension.

ii. When a heavier bob is attached, the downward force (weight) increases. As a result, the thread has to exert a greater upward pulling force to balance it. This increased pulling force causes more stretching in the thread. Hence, greater weight produces greater tension.

iii. When equal weights are placed on both sides, the tension on both sides becomes equal. The forces are balanced, so the net force on the system is zero. According to Newton’s first law of motion, the system remains at rest (equilibrium).

iv. The system moves toward the heavier side.

The heavier weight produces greater tension on its side. This creates an unbalanced force. The unbalanced force causes the system to accelerate toward the heavier side.

Very Short Answer Type Questions

Question 1.
What is the term for the multiplication of force or increase in speed provided by a machine?
Answer:
This multiplication is called Mechanical Advantage (MA).

Question 2.
State the formula for the mechanical advantage of a wheel and axle system.
Answer:
The formula is MA = \(\frac{\text { Radius of wheel }}{\text { Radius of axle }}\)

Question 3.
What is the SI unit of tension?
Answer:
The SI unit of tension is the newton (N).

Question 4.
When a system remains at rest because the upward tension equals the downward weight, what is this state called?
Answer:
This state is called equilibrium.

Question 14.
In which direction does tension always act relative to the object it is attached to?
Answer:
It always acts along the length of the string and pulls away from the object.

Short Answer Type Questions

Question 1.
Explain how a bicycle helps a cyclist gain speed without the cyclist being ‘extremely strong.’
Answer:
Bicycles use integrated systems like wheels, axles, and gears to help us multiply force or increase speed. This multiplication is known as Mechanical Advantage (MA). By pedaling, the cyclist applies a small input force that the machine transforms into a larger output force or higher speed at the wheels.

Question 2.
What is the difference between an ‘ideal machine’ and a ‘real machine’?
Or
Why is the efficiency of a real machine always less than 100%?
Answer:
An ideal machine is a theoretical model that is frictionless, meaning no energy is lost during operation. However, in a real machine, some input work is always lost to friction between the moving parts. Because the useful output work is less than the total input work, the efficiency (η) is always less than 100%.

Question 3.
Why is the steering wheel not made of same size of the axle?
Answer:
The steering wheel is deliberately made larger than the steering axle to get a high mechanical advantage. If both were made of equal size, steering a heavy vehicle would become very difficult.

Long Answer Type Questions

Question 1.
(i) Define the concept of Mechanical Advantage (MA) in your own words. Why is it referred to as a dimensionless quantity, and how does it help us classify a machine as a force multiplier or a speed multiplier?
(ii) Explain the practical utility of machines in daily life. Provide clear examples of how machines are used to overcome heavy loads, gain speed, and change the direction of effort for human convenience.
Answer:
(i) Definition Mechanical Advantage is a measure of the ‘help’ or leverage we get from using a machine. It describes how many times a machine multiplies the force we put into it. It is calculated by comparing the weight or resistance we are trying to move (the load) against the force we actually apply (the effort).

In physics, units usually define a quantity (like meters for length). However, mechanical advantage compares two forces. Since both the load and the effort are measured in the same unit (newton), these units cancel each other out during the comparison. This leaves us with a pure number, which is why we call it a dimensionless quantity.

Functional Classification:

Force Multiplier:
If the machine allows us to move a very heavy object using a small amount of strength, it is a force multiplier. In this case, the machine is amplifying our input force.

Speed Multiplier:
If the machine causes the object to move much faster or further than our own hands are moving, it is a speed multiplier. Here, we give up some of our strength to gain quickness.

Changing Direction: If the machine requires the same amount of force as the weight of the object, it isn’t multiplying force or speed. Instead, it is simply making the work more comfortable by letting us pull in a better direction.

(ii) Utility of Machines in General Life
Machines are used daily to make tasks easier, safer, or faster. Their utility is best understood through these three categories

1. To Overcome a Large Load (Force Multiplication)
Humans have physical limits, but machines help us bypass them.

Example – A Car Jack:
Lifting a car by hand is impossible. However, using a jack allows a person to apply a small amount of force over many strokes to lift a vehicle weighing thousands of kilograms.

Example – A Pliers:
When trying to cut a thick wire or grip a small bolt, our fingers aren’t strong enough. Pliers concentrate the force from our entire hand onto a tiny area, creating enough pressure to cut through metal.

2. To Gain Speed or Distance (Speed Multiplication)
Sometimes the goal is to finish a task quickly rather than moving something heavy.

Example – A Broom:
When you sweep the floor, your hands move only a small distance at the top of the handle, but the bristles at the bottom sweep across a large area of the floor very quickly.

Example – A Fishing Rod:
A fisherman moves the handle only a few inches, but the tip of the rod moves several feet through the air, allowing the hook to be thrown far into the water at high speed.

3. To Change the Direction of Effort
Gravity usually makes lifting things directly upward very difficult.

Example – A Pulley on a Flagpole:
To raise a flag to the top of a tall pole, you don’t have to climb it. By using a pulley, you can pull downwards on a rope. Pulling down is much easier because you can use your own body weight to help you, making the task feel light.

Question 2.
Two unequal masses m₁ and m₂ are connected over a frictionless pulley. If m₂ > m₁, derive the formula for the acceleration a (and tension T) of the system using Newton’s second law.
Answer:
For the heavier mass (m₂) the weight acts downward (m₂) and tension acts upward (T).
For the lighter mass (m₂) weight acts downward (m₁) and tension acts upward (T).
For m₂ (moving down),
m₂g -T = m₂a ………………….(i)
For m₁ (moving up),
T – m₁g = m₁a ……………..(ii)
Adding Eqs. (i) and (ii), we get
(m₂g – T) + (T – m₁g) = m₂a + m₁a
m₂g – m₁g = (m₁ + m₂) a
g (m₂ – m₁) = (m₁ + m₂) a
g (m₂ – m₁) = (m₁ + m₂) a
a = \(\frac{g\left(m_2-m_1\right)}{m_1+m_2}\)
This value put in Eq. (i),
m₂g – T = m₂a
T = m₂g – m₂a
= m₂g – m₂ \(\frac{g\left(m_2-m_1\right)}{m_1+m_2}\)
= m₂g \(\left[1-\frac{\left(m_2-m_1\right)}{\left(m_1+m_2\right)}\right]\)
= m₂g \(\left[\frac{m_1+m_2-m_2+m_1}{m_1+m_2}\right]\)
T = \(\frac{2 m_1 m_2 g}{m_1+m_2}\)

Question 3.
Two masses m₁ = 5 kg and m₂ = 4.8 kg tied to a string are hanging over a light friction less pulley. Find the acceleration of the masses when they are free to move.
Answer:
Acceleration of systems,
a = \(\left(\frac{m_2-m_1}{m_1+m_2}\right)\)
= \(\left(\frac{5-4.8}{5+4.8}\right)\) × 9.8 = 0.2 m/s²

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