PhysicsICSE Class 10 · Machines

Pulley Systems: Single Fixed, Single Movable and Block and Tackle, with MA, VR and η (ICSE Class 10)

Q: Why is the VR of a block and tackle equal to the number of pulleys?

Each pulley adds one strand supporting the movable block. If the load rises by d, every one of the n strands shortens by d, so the effort end must move nd: VR = n.

Q: Why does efficiency fall when more pulleys are added?

Each extra pulley adds friction, and extra pulleys in the movable block add weight that must be lifted every time. More of the input work is wasted, so η falls even though VR rises.

Q: Why should the upper block have more pulleys when the number is odd?

It keeps the lower, movable block lighter, so less energy is wasted lifting it, and the free end of the rope still comes off an upper pulley, so the effort acts downward.

Updated 15 October 2026 · Fact-checked

A single fixed pulley has VR = 1 and only changes the direction of the effort. A single movable pulley has VR = 2 and ideally halves the effort. A block and tackle of n pulleys has VR = n, ideal MA = n and practical MA = η × n, as n equal-tension strands hold the movable block.

Understand Pulley Systems: Fixed, Movable, Block and Tackle

A pulley is a wheel with a grooved rim, free to turn on an axle held in a frame (the block). A rope passing over it is the tackle. If the rope is light and the pulleys frictionless, the tension T is the same all along one continuous rope, and the effort equals that tension: $E = T$ .

1. Single fixed pulley. The block is fixed to a rigid support. The load hangs from one end of the rope; the effort pulls the other end down.

The load and effort move the same distance: $V R = 1$ .
Ideally $L = T = E$ , so $M A = 1$ . With friction, $E > L$ , so in practice $M A < 1$ and $η < 1$ .
Use: it changes the direction of the effort to a convenient downward pull, so you can use your own weight. Examples: raising a flag, drawing water from a well.

2. Single movable pulley. One end of the rope is tied to a rigid support; the rope passes under the pulley, which carries the load, and the effort pulls the free end upward.

Two strands support the pulley. If the load rises by $d$ , each strand shortens by $d$ , so the effort moves $2 d$ : $V R = 2$ .
With negligible friction and pulley weight $w$ : $2 T = L + w$ and $E = T$ , so $E = \frac{L + w}{2}$ . Ideally ( $w = 0$ ) $M A = 2$ .
Use: a force multiplier, but the effort acts upward, which is inconvenient. Adding a fixed pulley above it turns the effort downward without changing VR.

3. Block and tackle. An upper fixed block hangs from a rigid support and a lower movable block carries the load. One continuous rope passes round all the pulleys in turn.

If there are $n$ pulleys in total, $n$ strands support the movable block. Raising the load by $d$ shortens each strand by $d$ , so the effort moves $n d$ : $V R = n$ .
With negligible friction and movable block weight $w$ : $n T = L + w$ , $E = T = \frac{L + w}{n}$ , so $M A = \frac{n L}{L + w}$ (ideal $M A = n$ when $w = 0$ ).
In general, practical $M A = η \times n$ .

Effect of the movable block's weight. With friction negligible, $η = \frac{M A}{V R} = \frac{L}{L + w}$ . So:

a heavier movable block (more pulleys in it) lowers η;
a heavier load raises η, because the fixed waste of lifting the block becomes a smaller share.

Friction in more pulleys also lowers η, which is why adding pulleys raises VR but reduces efficiency.

Sharing the pulleys. For an even $n$ , the two blocks have equal numbers of pulleys and the free end of the rope is tied to the hook of the upper block. For an odd $n$ , the upper block has one pulley more than the lower one and the rope's free end is tied to the hook of the lower block. Keeping more pulleys in the upper block keeps the movable block light (higher η), and the effort still comes off an upper pulley, pulling downward.

Drawing a block and tackle (what examiners check). Draw a rigid support at the top and hang the upper block from it. Join the pulleys of each block on one frame or axle, with hooks on the frames, never on the rims. Keep every strand vertical, straight and taut. Mark an upward arrow T on every strand supporting the movable block (the same T on each, not $T_{1}$ , $T_{2}$ , $T_{3}$ ), the load L hanging from the lower hook, and the effort E as a downward arrow on the free end.

Advantage over a single movable pulley. A much larger VR and MA, so a much smaller effort for the same load, with the effort in the convenient downward direction.

Pulley Systems: Fixed, Movable, Block and Tackle: formulas and key facts

Single fixed pulley: $V R = 1, M A_{ideal} = 1$; Practical MA < 1; changes direction only.
Single movable pulley: $V R = 2, E = \frac{L + w}{2}$; Friction negligible; w = weight of the pulley.
Block and tackle: $V R = n, E = T = \frac{L + w}{n}$; n = total pulleys = strands supporting the movable block.
Practical MA: $M A = η \times V R$; Use η as a decimal.
Efficiency with block weight only: $η = \frac{L}{L + w}$; Friction negligible: η rises with load, falls with block weight.

How to solve Pulley Systems: Fixed, Movable, Block and Tackle questions

Count the supporting strands first; that number is the VR and fixes all the distances.

1Identify the system and write VR: 1 (fixed), 2 (movable) or n (block and tackle).
2If η is given: $M A = η \times V R$ , then $E = \frac{L}{M A}$ .
3If friction is negligible but the movable block has weight $w$ : $E = \frac{L + w}{n}$ , then $M A = \frac{L}{E}$ and $η = \frac{M A}{V R}$ .
4Distance moved by the effort $= V R \times$ distance moved by the load.
5For work: $W_{i} = E \times d_{E}$ , $W_{o} = L \times d_{L}$ .
6For a diagram, decide the pulleys in each block from n (odd: one more in the upper block) and mark T, L and E.

Pulley Systems: Fixed, Movable, Block and Tackle in real life

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.

Raising a flag with a fixed pulley

Suppose a school flag and its rope weigh 15 N, and because of friction at the pulley at the top of the pole the student must pull with 18 N.

Find the MA and efficiency. Why use the pulley at all?

Try it first, then show the solutionSolution

$M A = \frac{15}{18} \approx 0.83$ .
$V R = 1$ , so $η \approx 0.83 = 83%$ .

Answer: MA ≈ 0.83, η ≈ 83%. The pulley lets the student pull down from the ground instead of climbing the pole.

Memory hook: A fixed pulley sells you direction, not force.

Lifting a gearbox in a garage

Imagine a mechanic uses a block and tackle of 4 pulleys whose movable block weighs 50 N to lift a 750 N gearbox. Friction is negligible.

Find the effort, the MA and the efficiency.

Try it first, then show the solutionSolution

$E = \frac{750 + 50}{4} = 200$ N.
$M A = \frac{750}{200} = 3.75$ .
$η = \frac{3.75}{4} = 0.9375 \approx 94%$ , which equals $\frac{750}{800}$ .

Answer: 200 N; MA 3.75; η ≈ 94%.

Memory hook: The lower block is a load you lift every time: keep it light.

Tricks to remember Pulley Systems: Fixed, Movable, Block and Tackle

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

Count the strands, not the wheels on top
VR = the number of strands holding up the movable block, which equals the total number of pulleys in a block and tackle.
Use it when: Finding VR from a diagram.
Odd? Top gets one more
Odd VR: the upper block has the extra pulley and the rope is tied to the lower block. Even VR: equal blocks, rope tied to the upper block.
Use it when: Drawing a block and tackle for a given VR.
One rope, one T
One continuous rope has one tension. Label every strand T.
Use it when: Avoiding the T₁, T₂, T₃ error in diagrams.
1, 2, n
Fixed 1, movable 2, block and tackle n: the VRs count up.
Use it when: MCQs and quick recall.

Pulley Systems: Fixed, Movable, Block and Tackle: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: VR from the pulleys · 1 mark · MCQBoard level

A block and tackle has 3 pulleys in the upper block and 2 in the lower block. Its velocity ratio is:
(a) 2
(b) 3
(c) 5
(d) 6

Try it first, then show the solutionSolution

VR = total number of pulleys $= 3 + 2 = 5$ .

Answer: (c) 5

Example 2: A real single fixed pulley · 3 marks · Short answerBoard level

An effort of 520 N is needed to raise a load of 500 N with a single fixed pulley. (a) Find the MA, VR and efficiency. (b) Why is MA less than 1 here? (c) Why is the pulley still used?

Try it first, then show the solutionSolution

(a) $M A = \frac{500}{520} \approx 0.96$ ; $V R = 1$ ; $η \approx 96%$ . (1)
(b) Part of the effort is used to overcome friction at the axle. (1)
(c) It changes the direction of the effort to a convenient downward pull. (1)

Answer: (a) MA ≈ 0.96, VR = 1, η ≈ 96% (b) Friction (c) Convenient direction of effort

Example 3: Single movable pulley with its own weight · 3 marks · Short answerHarder board level

A single movable pulley weighs 40 N and friction is negligible. It is used to raise a load of 460 N. Find (a) the effort, (b) the MA, (c) the efficiency.

Try it first, then show the solutionSolution

Two strands support load and pulley: $2 E = 460 + 40$ . (½)
(a) $E = 250$ N. (½)
(b) $M A = \frac{460}{250} = 1.84$ . (1)
(c) $η = \frac{1.84}{2} = 0.92 = 92%$ . Check: $\frac{460}{460 + 40} = 0.92$ . (1)

Answer: (a) 250 N (b) 1.84 (c) 92%

Example 4: Block and tackle of VR 3 · 4 marks · Long answerHarder board level

(a) Describe how you would draw a block and tackle with VR = 3, so that the effort acts downward. (b) It works at 80% efficiency and raises a load of 900 N through 2 m. Find its MA, the effort, and how much rope must be pulled in.

Try it first, then show the solutionSolution

(a) Upper block with 2 pulleys hung from a rigid support; lower movable block with 1 pulley carrying L. Tie one end of the rope to the hook of the lower block, take it up over an upper pulley, down under the lower pulley, up over the second upper pulley and down to the effort E. Three vertical strands support the lower block; mark T upward on each and E downward on the free end. (2)
(b) $M A = 0.8 \times 3 = 2.4$ . (½)
$E = \frac{900}{2.4} = 375$ N. (1)
Rope pulled $= 3 \times 2 = 6$ m. (½)

Answer: (a) 2 pulleys above, 1 below, rope tied to the lower block (b) MA 2.4, 375 N, 6 m

Example 5: Why efficiency rises with load · 4 marks · Long answerHOTS / competency

A block and tackle has 6 pulleys. Its movable block weighs 60 N and friction is negligible. Find the effort, MA and efficiency for loads of (a) 540 N and (b) 1140 N. (c) What do the results show?

Try it first, then show the solutionSolution

(a) $E = \frac{540 + 60}{6} = 100$ N; $M A = 5.4$ ; $η = \frac{5.4}{6} = 90%$ . (1½)
(b) $E = \frac{1140 + 60}{6} = 200$ N; $M A = 5.7$ ; $η = 95%$ . (1½)
(c) VR stays 6, but MA and η rise with load: the 60 N block is a smaller share of what is lifted ( $η = \frac{L}{L + w}$ ). (1)

Answer: (a) 100 N, 5.4, 90% (b) 200 N, 5.7, 95% (c) η increases with load; VR does not change.

Example 6: Case study: lifting an engine · 4 marks · Case-basedHOTS / competency

A mechanic weighing 550 N wants to lift a 2400 N engine using a block and tackle of 5 pulleys, by hanging her weight on the rope. The effort needed is 600 N.
(a) How should the 5 pulleys be shared, and where is the rope tied?
(b) Find the MA and efficiency.
(c) Can she lift the engine by her weight alone?
(d) After the pulleys are cleaned and oiled, the efficiency rises to 92%. Can she lift it now?

Try it first, then show the solutionSolution

(a) 3 pulleys in the upper fixed block, 2 in the lower movable block; the rope is tied to the lower block, so the free end leaves an upper pulley downward. (1)
(b) $M A = \frac{2400}{600} = 4$ ; $η = \frac{4}{5} = 80%$ . (1)
(c) No: her weight, 550 N, is less than the 600 N needed. (1)
(d) $M A = 0.92 \times 5 = 4.6$ ; $E = \frac{2400}{4.6} \approx 522$ N, less than 550 N, so yes. (1)

Answer: (a) 3 above, 2 below, rope tied to the lower block (b) MA 4, η 80% (c) No (d) Yes, E ≈ 522 N

Where students lose marks in Pulley Systems: Fixed, Movable, Block and Tackle

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

Mistake: Careless block and tackle diagrams
Marks go for a rigid support, clear fixed and movable blocks, hooks on frames, taut vertical strands and labelled L, E and T.
Wrong working
Strands labelled $T_{1}$ , $T_{2}$ , $T_{3}$ ; hooks drawn on the rims; no support at the top.
Right working
One label T on every supporting strand, hooks on the block frames, a rigid support drawn.
Do this: Practise drawing VR 2, 3, 4 and 5 until each takes a minute.
Usually costs: Reported by CISCE examiners for both 2024 Q6(iii) and 2025 Q7(i).
Mistake: Using the ideal MA when η is given
A practical system's MA is η × VR.
Wrong working
VR 4, η 70%, L 560 N: $E = \frac{560}{4} = 140$ N.
Right working
$M A = 0.7 \times 4 = 2.8$ , so $E = \frac{560}{2.8} = 200$ N.
Do this: Write $M A = η \times V R$ as the first line.
Usually costs: Reported for 2024 Q6(iii).
Mistake: Giving only 'convenient direction' as the advantage of a block and tackle
A single fixed pulley also gives a convenient direction; the block and tackle's real gain over a single movable pulley is a larger VR and MA, so less effort.
Wrong working
'It lets you use your own weight.'
Right working
'It has a much larger VR and MA, so the effort needed is far smaller, and the effort can act downward.'
Do this: Name the quantity that increases.
Usually costs: Reported for 2024 Q2(iv).
Mistake: Repeating the same reason for 'why more pulleys in the upper block?'
This asks about the two blocks of one system, not about the system versus a single pulley.
Wrong working
'Because it increases MA.'
Right working
'It keeps the movable block light, so less energy is wasted lifting it and η is higher; the effort also stays downward.'
Do this: Link the answer to the weight of the lower block and efficiency.
Usually costs: Also reported for 2024 Q2(iv).

Exam tips

In 2024 Q6(iii) (VR 2, load 48 kgf, η 80%) the scheme expected $\frac{80}{100} = \frac{M A}{2}$ , $M A = 1.6$ , then $E = \frac{48}{1.6} = 30$ kgf, with MA written as a decimal and no unit.
When asked to draw for a given VR, first write how many pulleys go in each block, then draw; the 2025 examiners asked for T marked on every strand.
State the reason for $η < 1$ in pulleys precisely: friction at the axles and the weight of the movable block (and rope).
Keep loads in kgf if the question uses kgf; do not mix kgf and N.

Practice questions on Pulley Systems: Fixed, Movable, Block and Tackle

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

Q1 · 1 mark · MCQBoard level
In an ideal block and tackle, the tension in each strand of the rope is:
(a) different in every strand
(b) the same, and equal to the effort
(c) half the load
(d) equal to the load
Hint
It is one continuous rope.
Answer
(b) the same, and equal to the effort
Q2 · 3 marks · Short answerBoard level
State the VR and the ideal MA of (a) a single fixed pulley, (b) a single movable pulley. Give one advantage of each.
Hint
Count the strands supporting the load.
Answer
(a) VR 1, ideal MA 1; changes the effort to a convenient downward direction. (b) VR 2, ideal MA 2; halves the effort (ideally), so it is a force multiplier.
Q3 · 3 marks · Short answerHarder board level
Describe a block and tackle of VR 5: the pulleys in each block, where the rope is tied, and the labels you would mark.
Hint
Odd VR: the upper block gets the extra pulley.
Answer
3 pulleys in the upper block (hung from a rigid support) and 2 in the lower block. The rope is tied to the hook of the lower block and passes alternately over upper and under lower pulleys, leaving the last upper pulley downward. Mark the same T upward on each of the 5 supporting strands, L on the lower hook and E downward on the free end.
Q4 · 3 marks · Short answerHarder board level
A single movable pulley has an efficiency of 85%. It raises a 340 N load through 3 m. Find (a) the effort, (b) the work done by the effort, (c) the useful work done.
Hint
$M A = η \times 2$ ; the effort moves twice as far as the load.
Answer
(a) $M A = 1.7$ , $E = \frac{340}{1.7} = 200$ N. (b) $W_{i} = 200 \times 6 = 1200$ J. (c) $W_{o} = 340 \times 3 = 1020$ J.
Q5 · 3 marks · Short answerHarder board level
With a block and tackle, an effort of 300 N moves through 12 m while a load of 1500 N rises 2 m. Find the VR, the MA and the efficiency, and state how many pulleys the system has.
Hint
VR = number of pulleys.
Answer
$V R = \frac{12}{2} = 6$ (6 pulleys); $M A = \frac{1500}{300} = 5$ ; $η = \frac{5}{6} \approx 83.3%$ .
Q6 · 3 marks · Short answerHarder board level
Two block and tackle systems A and B both have VR 4 and negligible friction. A's movable block weighs 40 N and B's weighs 80 N. Each lifts a 440 N load. Find the effort and efficiency of each, and say which design is better.
Hint
$E = \frac{L + w}{n}$ ; $η = \frac{L}{L + w}$ .
Answer
A: $E = \frac{480}{4} = 120$ N, $η = \frac{440}{480} \approx 91.7%$ . B: $E = \frac{520}{4} = 130$ N, $η = \frac{440}{520} \approx 84.6%$ . A is better: a lighter movable block wastes less energy.
Q7 · 4 marks · Long answerHOTS / competency
(a) For a block and tackle of n pulleys with negligible friction and a movable block of weight w, show that $η = \frac{L}{L + w}$ . (b) For n = 4 and w = 50 N, find the least load for which the efficiency is at least 90%.
Hint
Start from $n E = L + w$ .
Answer
(a) $n E = L + w$ , so $M A = \frac{L}{E} = \frac{n L}{L + w}$ and $η = \frac{M A}{n} = \frac{L}{L + w}$ . (b) $\frac{L}{L + 50} \geq 0.9$ gives $0.1 L \geq 45$ , so $L \geq 450$ N.

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.VR of a block and tackle with 7 pulleys?Show answer
7.
2.Ideal MA of a single movable pulley?Show answer
2.
3.Direction of the effort on a single movable pulley?Show answer
Upward (inconvenient).
4.Which pulley system only changes the direction of the effort?Show answer
A single fixed pulley.
5.If the effort on a block and tackle is 150 N, what is the tension in each strand (friction negligible)?Show answer
150 N.

Pulley Systems: Fixed, Movable, Block and Tackle: frequently asked questions

Why is the VR of a block and tackle equal to the number of pulleys?

Each pulley adds one strand supporting the movable block. If the load rises by d, every one of the n strands shortens by d, so the effort end must move nd: VR = n.

Why does efficiency fall when more pulleys are added?

Each extra pulley adds friction, and extra pulleys in the movable block add weight that must be lifted every time. More of the input work is wasted, so η falls even though VR rises.

Why should the upper block have more pulleys when the number is odd?

It keeps the lower, movable block lighter, so less energy is wasted lifting it, and the free end of the rope still comes off an upper pulley, so the effort acts downward.