Machines ICSE Class 10: Mechanical Advantage, Velocity Ratio, Levers and Pulleys

What Machines is about

Weightage: CISCE publishes no chapter or unit weightage for ICSE Physics. Machines is in the 1. Force, Work, Power and Energy (v) part of the 2027 syllabus and can be asked in both Section A and Section B of the 80-mark paper.Source: CISCE ICSE Physics (Science Paper 1) syllabus, examination year 2027

Key concepts

Load, effort and what machines do

• Load ($L$): the resistance the machine overcomes (a weight to lift).
• Effort ($E$): the force applied to the machine.

A machine may be used:
1. as a force multiplier (a jack lifts a car with a small effort);
2. to change the point of application of the effort;
3. to change the direction of the effort to a convenient one (a single fixed pulley);
4. to gain speed or distance (a pair of scissors with long blades, the human forearm).

You cannot gain both force and distance at once: what is gained in force is lost in distance.

Worked example

Give the main purpose of (a) a car jack, (b) a single fixed pulley at the top of a flagpole, (c) a pair of sugar tongs.

Try it first, then show the solutionSolution

1. (a) To multiply force: a small effort lifts a heavy car.
2. (b) To change the direction of effort: pull down to raise the flag.
3. (c) To gain distance and fine control (effort less than force on load is not the aim).

Answer: (a) force multiplier (b) change of direction (c) gain in distance / control

MA, VR and efficiency

• Mechanical advantage: $MA=\frac{L}{E}$ (no unit).
• Velocity ratio: $VR=\frac{d_E}{d_L}=\frac{V_E}{V_L}$, the distance (or speed) of the effort divided by that of the load in the same time (no unit).
• Work input $W_i=E\times d_E$; work output $W_o=L\times d_L$.
• Efficiency: $\eta =\frac{W_o}{W_i}$, often given as a percentage.

VR depends only on the design of the machine; MA also depends on friction and the weight of moving parts.

Worked example

A machine lifts a load of 600 N with an effort of 200 N. The effort moves 4 m while the load rises 1 m. Find MA, VR and efficiency.

Try it first, then show the solutionSolution

1. $MA=\frac{600}{200}=3$.
2. $VR=\frac{4}{1}=4$.
3. $\eta =\frac{600\times 1}{200\times 4}=\frac{600}{800}=0.75=75\%$.

Answer: MA = 3, VR = 4, η = 75%

Relation η = MA/VR; ideal and practical machines

Derivation: $\eta =\frac{W_o}{W_i}=\frac{L\times d_L}{E\times d_E}=\frac{L}{E}\times \frac{d_L}{d_E}=MA\times \frac{1}{VR}$, so
$\eta =\frac{MA}{VR}$, i.e. $MA=\eta \times VR$.

An ideal machine has $\eta =1$ (100%) and $MA=VR$. In every practical machine some input energy is wasted against friction and in lifting moving parts, so $\eta <1$ and $MA<VR$.

Worked example

A machine has VR 5 and efficiency 80%. Find its MA, and the effort needed to lift 1000 N.

Try it first, then show the solutionSolution

1. $MA=0.8\times 5=4$.
2. $E=\frac{1000}{4}=250$ N.

Answer: MA = 4; E = 250 N

Levers and their three classes

A lever is a rigid bar that turns about a fixed point, the fulcrum $F$. By the principle of moments (ideal lever):
$L\times \text{load arm}=E\times \text{effort arm}$, so $MA=\frac{\text{effort arm}}{\text{load arm}}=VR$.

• Class I (fulcrum between load and effort): see-saw, scissors, crowbar, pliers, beam balance. MA can be more than, equal to, or less than 1.
• Class II (load between fulcrum and effort): nutcracker, wheelbarrow, bottle opener. Effort arm is always longer: MA > 1.
• Class III (effort between fulcrum and load): human forearm, fire tongs, sugar tongs, fishing rod. Effort arm is always shorter: MA < 1, but the load moves farther and faster.

In the human body: nodding the head (class I, neck as fulcrum), raising the body on the toes (class II), lifting a weight with the forearm (class III).

Worked example

A crowbar 1.5 m long is used to lift a 900 N stone, with the fulcrum 0.3 m from the stone end. Find the MA and the least effort. Which class is it?

Try it first, then show the solutionSolution

1. Load arm $=0.3$ m; effort arm $=1.2$ m.
2. $MA=\frac{1.2}{0.3}=4$; $E=\frac{900}{4}=225$ N.
3. Fulcrum between load and effort: class I.

Answer: MA = 4; 225 N; class I

Single fixed and single movable pulleys

Single fixed pulley (axle fixed to a support): the load hangs from one end of the rope and the effort pulls the other end.

• Ideal $MA=1$, $VR=1$. In practice $MA<1$.
• Use: changes the direction of effort to a convenient downward pull; you can use your own weight.

Single movable pulley (pulley moves with the load; one end of the rope fixed to a support, effort pulls the other end upwards):

• Two strands support the load, so $VR=2$ and ideal $MA=2$.
• Use: halves the effort (ideally), but the effort acts upwards, an inconvenient direction.

In practice the weight of a movable pulley and friction reduce MA.

Worked example

A single movable pulley of efficiency 80% lifts a load of 200 N. Find the MA and the effort.

Try it first, then show the solutionSolution

1. $VR=2$, so $MA=0.8\times 2=1.6$.
2. $E=\frac{200}{1.6}=125$ N.

Answer: MA = 1.6; E = 125 N

Block and tackle

A block and tackle has an upper fixed block and a lower movable block of pulleys, with one continuous rope (the tackle) going round all of them. The load hangs from the movable block.

• $VR=n$, the total number of pulleys = the number of rope strands supporting the movable block.
• Ideal $MA=n$; practical $MA=\eta \times n$.
• The tension is the same in every strand (it is one rope), equal to the effort.
• For an odd $n$, the fixed block has one more pulley than the movable block, so the effort can be applied downwards (convenient). For an even $n$, both blocks have equal numbers.

Advantage over a single movable pulley: a much larger MA with the effort in a convenient direction. Efficiency falls as more pulleys are added, because there is more friction and a heavier movable block.

Worked example

A block and tackle with 4 pulleys has efficiency 75%. Find the effort to raise a 300 N load, and how far the effort moves when the load rises 2 m.

Try it first, then show the solutionSolution

1. $VR=4$; $MA=0.75\times 4=3$.
2. $E=\frac{300}{3}=100$ N.
3. Effort distance $=VR\times d_L=4\times 2=8$ m.

Answer: 100 N; 8 m

Effect of the weight of the movable block

If friction is negligible but the movable block has weight $w$, the $n$ strands together support $L+w$:
$n\times E=L+w$, so $E=\frac{L+w}{n}$ and $MA=\frac{L}{E}=\frac{nL}{L+w}<n$.

The heavier the load compared with the block, the closer MA gets to VR, so efficiency increases with load.

Worked example

A frictionless block and tackle has 4 pulleys and a movable block of weight 20 N. Find the effort, MA and efficiency for a load of 380 N.

Try it first, then show the solutionSolution

1. $E=\frac{380+20}{4}=100$ N.
2. $MA=\frac{380}{100}=3.8$.
3. $\eta =\frac{3.8}{4}=0.95=95\%$.

Answer: E = 100 N, MA = 3.8, η = 95%

Physics in real life: Machines

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Topics in this chapter

• Mechanical Advantage, Velocity Ratio and Efficiency
• Levers and Their Classes
• Pulley Systems: Fixed, Movable, Block and Tackle

Machines formula sheet

Mechanical advantage

$MA=\frac{L}{E}$

No unit; write as a decimal.

Velocity ratio

$VR=\frac{d_E}{d_L}=\frac{V_E}{V_L}$

Fixed by the design.

Efficiency

$\eta =\frac{W_o}{W_i}=\frac{MA}{VR}$

η < 1 for practical machines.

Lever (ideal)

$L\times \text{load arm}=E\times \text{effort arm}$

MA = effort arm ÷ load arm.

Pulleys

$\text{fixed: }VR=1;\text{movable: }VR=2;\text{block and tackle: }VR=n$

n = number of pulleys = strands supporting the lower block.

Block and tackle with a heavy lower block

$E=\frac{L+w}{n}$

Frictionless; w = weight of the movable block.

Machines: diagrams to practise

Practise each one on paper: draw it from the checklist, then tick off every label.

How the board asks Machines

The question patterns to expect, and the method that works for each.

Tricks to remember Machines

Short memory aids. Say each one aloud once, then use it on a question the same day.

• 1-2-3: F-L-E in the middle

  Class I: Fulcrum in the middle; Class II: Load in the middle; Class III: Effort in the middle.

  Use it when: Classifying levers.

• η = MA ÷ VR

  Efficiency is how much of the ideal MA you actually get.

  Use it when: Every machine numerical.

• Count the strands

  VR of a pulley system = number of strands holding up the movable block.

  Use it when: Block and tackle.

• Odd? Upper gets one more

  For odd VR, put the extra pulley in the fixed block so you can pull down.

  Use it when: Drawing block and tackle systems.

Machines: board-level solved questions

Ordered from board level to HOTS. Cover the solution, write your own, then compare step by step.

Case-study practice (Section B style)

Read the situation, then answer every part. In the board paper this is a 10-mark question split into 3 + 3 + 4 marks.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Where students lose marks in Machines

The slips examiners see most often, and what to write instead.

• ✗Mistake: Classifying levers by memory, not position

  CISCE examiners' comments, 2024: the concept of classes of levers was unclear, and some candidates drew wrong diagrams that were not asked for.

  ✓Do this: Sketch the lever and see what lies in the middle: F (class I), L (II) or E (III).

  Usually costs: 1 mark.

• ✗Mistake: Vague advantages of a block and tackle

  CISCE examiners' comments, 2024: candidates gave only 'convenient direction' as the advantage over a single movable pulley, and in the next part repeated it instead of explaining why more pulleys go in the upper (fixed) block.

  ✓Do this: Advantage: much larger MA (and VR) with a convenient effort direction. More pulleys in the fixed block (odd VR) let the effort act downwards.

  Usually costs: 1 mark each.

• ✗Mistake: Poor block and tackle diagrams

  CISCE examiners' comments, 2024 and 2025: no rigid support, unclear fixed and movable blocks, hooks on the rims, bulging or loose strands, no effort or tension arrows, and tensions labelled T₁, T₂, T₃ though the tension is the same throughout.

  ✓Do this: Follow the diagram checklist and mark the same T on every strand.

  Usually costs: Up to 2 marks.

• ✗Mistake: MA as a fraction, with a unit, or ideal

  CISCE examiners' comments, 2024: candidates left M.A. as 8/5 instead of 1.6, wrote a unit for M.A., used the ideal M.A. when efficiency was given, and confused kgf with N.

  ✓Do this: MA = η × VR, written as a decimal with no unit; keep effort in the same unit as the load.

  Usually costs: 1 mark each.

• ✗Mistake: Misreading a load–effort graph

  CISCE examiners' comments, 2025: for a graph of load (y-axis) against effort (x-axis), candidates took the slope as x over y and chose 1/MA.

  ✓Do this: Slope = change in y ÷ change in x = load ÷ effort = MA.

  Usually costs: 1 mark.

• ✗Mistake: Judging MA by the effort arm alone

  CISCE examiners' comments, 2025: comparing three levers, candidates picked the longest effort arm instead of comparing the effort arm with the load arm of the same lever.

  ✓Do this: MA = effort arm ÷ load arm; compare the ratio, not one length.

  Usually costs: 1 to 2 marks.

Practice questions on Machines

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQBoard level

   The velocity ratio of a single movable pulley is:
   (a) 1
   (b) 2
   (c) 0.5
   (d) 4

   Hint

   Two strands support it.

   Answer

   (b)

2. Q2 · 1 mark · MCQBoard level

   In which class of lever is the mechanical advantage always less than 1?
   (a) class I
   (b) class II
   (c) class III
   (d) none

   Hint

   Effort in the middle.

   Answer

   (c)

3. Q3 · 1 mark · MCQHarder board level

   A machine has velocity ratio 5 and efficiency 80%. Its mechanical advantage is:
   (a) 0.16
   (b) 4
   (c) 6.25
   (d) 400

   Hint

   MA = η × VR.

   Answer

   (b)

4. Q4 · 1 mark · Assertion-reasonBoard level

   Assertion (A): A single fixed pulley is often used even though its ideal MA is 1.
   Reason (R): It changes the direction of the effort to a more convenient one.
   (a) (A) is true and (R) is false.
   (b) (A) is false and (R) is true.
   (c) Both (A) and (R) are true, and (R) is the correct explanation for (A).
   (d) Both (A) and (R) are true, but (R) is not the correct explanation for (A).

   Hint

   Why use it at all?

   Answer

   (c)

5. Q5 · 2 marks · Very short answerHarder board level

   Give one example from the human body of (a) a class I lever, (b) a class II lever.

   Hint

   Head and toes.

   Answer

   (a) Nodding the head (neck joint as fulcrum) (b) Raising the body on the toes

6. Q6 · 2 marks · Short answerHarder board level

   Explain why scissors for cutting metal have short blades and long handles, while scissors for cutting cloth have long blades.

   Hint

   Compare effort arm and load arm.

   Answer

   Metal: effort arm (handles) longer than load arm (blades): MA > 1, so a large cutting force. Cloth: long blades make MA < 1 but the blade tips move farther and faster, for long quick cuts.

7. Q7 · 3 marks · Long answerBoard level

   Define (a) mechanical advantage, (b) velocity ratio, (c) efficiency of a machine. Which of these has a unit?

   Hint

   All are ratios.

   Answer

   (a) MA = load ÷ effort. (b) VR = distance moved by effort ÷ distance moved by load. (c) η = work output ÷ work input. None has a unit (η may be given as a percentage).

8. Q8 · 3 marks · Long answerHarder board level

   A pair of fire tongs is 30 cm long. The hand presses 10 cm from the hinge and a piece of coal weighing 3 N is held at the tips. Find the effort, the MA and the class of lever. Why are tongs designed this way?

   Hint

   Moments about the hinge; the effort lies between the hinge and the load.

   Answer

   $E\times 10=3\times 30$, so $E=9$ N; $MA=\frac{3}{9}\approx 0.33$; class III (effort in the middle). The MA is less than 1, but the long arms keep the hand away from the fire and the tips move farther, giving reach and control.

9. Q9 · 4 marks · Long answerHOTS / competency

   Draw a block and tackle with VR = 4, showing where the end of the rope is tied and the direction of the effort. If it lifts a load of 600 N with efficiency 75%, find the MA, the effort and the length of rope pulled to raise the load by 1.5 m.

   Hint

   Two pulleys in each block; four strands support the movable block.

   Answer

   Two pulleys in the fixed block and two in the movable block; the rope is tied to the hook of the fixed block, passes round all four pulleys and leaves the fixed block, so the effort acts downwards; the same tension T in each of the four supporting strands. $MA=0.75\times 4=3$; $E=\frac{600}{3}=200$ N; rope pulled $=4\times 1.5=6$ m.

10. Q10 · 3 marks · Long answerHarder board level

    A single movable pulley has efficiency 90%. Find the effort needed to lift a 360 N load, and the work done by the effort to raise the load 2 m.

    Hint

    VR = 2.

    Answer

    $MA=0.9\times 2=1.8$; $E=\frac{360}{1.8}=200$ N; the effort moves $2\times 2=4$ m, so $W=200\times 4=800$ J (useful work $360\times 2=720$ J).

11. Q11 · 1 mark · MCQHOTS / competency

    In a class I lever with the fulcrum exactly at the middle, the mechanical advantage is:
    (a) less than 1
    (b) equal to 1
    (c) greater than 1
    (d) zero

    Hint

    Equal arms.

    Answer

    (b)

12. Q12 · 4 marks · Long answerHOTS / competency

    (a) Why does the efficiency of a block and tackle decrease when more pulleys are added? (b) Why does its efficiency increase when a heavier load is lifted with the same system? (c) A frictionless 4-pulley system has a 20 N movable block; find its efficiency for a 180 N load.

    Hint

    E = (L + w)/n.

    Answer

    (a) More friction and a heavier movable block waste more energy. (b) The wasted work on the block is the same, so it is a smaller fraction of a larger useful output. (c) $E=\frac{200}{4}=50$ N; $MA=3.6$; $\eta =90\%$.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.Define mechanical advantage.Show answer

   Ratio of load to effort, MA = L/E.

2. 2.Define velocity ratio.Show answer

   Ratio of the distance moved by the effort to the distance moved by the load.

3. 3.Relation between η, MA and VR?Show answer

   η = MA/VR

4. 4.Which lever always has MA > 1?Show answer

   Class II.

5. 5.Which lever always has MA < 1?Show answer

   Class III.

6. 6.VR of a single movable pulley?Show answer

   2

7. 7.VR of a block and tackle with n pulleys?Show answer

   n

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Can you derive η = MA/VR?
• ☐Can you classify ten levers by sketching them?
• ☐Do you write MA as a decimal with no unit?
• ☐Can you draw a block and tackle for VR 3 and VR 4?
• ☐Can you explain why MA < VR?
• ☐Can you explain why η rises with load?

Machines: frequently asked questions