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GATE Engineering Mechanics (Statics & Dynamics): practice questions

GATE — Agricultural Engineering (AG) · India · IITs and IISc on rotation (2026: IIT Guwahati)

Original practice questions written to the published syllabus · not past papers
10worked here, free
17written to this exam in this subject
8syllabus units

About GATE

GATE — Agricultural Engineering (AG) is a postgraduate admission exam run by IITs and IISc on rotation (2026: IIT Guwahati), for candidates in India. Computer-based, 3 hours, 100 marks (15 General Aptitude + 85 technical: 25 one-mark and 30 two-mark questions). MCQ, MSQ and NAT; negative marking on MCQ only (−1/3 for one-mark, −2/3 for two-mark); no partial credit on MSQ. On-screen virtual calculator.

Source: gate2026.iitg.ac.in.

Checked against the exam body's published information. Formats and fees change; confirm the current edition there before you book.

Engineering Mechanics (Statics & Dynamics) in GATE

Engineering mechanics is not a named section, but its methods carry the tractor questions: weight transfer, axle loads and CG location, traction and slip, stability and overturning, and belt-drive power in machine design.

Forces, equilibrium and motion of particles and rigid bodies: the starting point for structures, machines and tractor mechanics.

Our 17 GATE questions in this subject: 0 easy, 8 medium, 9 hard, across 8 units.

10 practice questions, worked

Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.

These 10 were written to GATE and are not shown on any other exam's page.

Question 1 · medium

A tractor with a 2.25 m wheelbase pulls a horizontal drawbar load of 12 kN at a steady speed from a hitch point 0.45 m above the ground. How much load does the pull transfer from the front axle to the rear axle?

  1. 2.40 kN
  2. 60.00 kN
  3. 5.40 kN
  4. 12.00 kN
Answer and working

A. 2.40 kN

Taking moments about the rear-wheel contact, the pull adds a moment P h that lifts the front: transfer = P h / L = 12 x 0.45 / 2.25 = 2.40 kN. Multiplying by L/h (60.00 kN) inverts the arms; 5.40 is a moment in kN m, not a force.

Question 2 · hard

In a simple rigid static model, a 2200 kg tractor has its centre of gravity 0.8 m ahead of the rear axle and pulls horizontally from a hitch 0.55 m high. At what drawbar pull does the front-axle load fall to zero?

  1. 14.8 kN
  2. 3.20 kN
  3. 31.4 kN
  4. 21.6 kN
Answer and working

C. 31.4 kN

Front reaction Rf L = W x - P h, so Rf = 0 when P = W x / h = 21.58 x 0.8 / 0.55 = 31.4 kN. Swapping x and h gives 14.8 kN; using mass instead of weight gives 3.20. In practice the front lifts at lower pulls when the hitch is higher, the wheels stall or the tractor faces uphill. 21.6 kN is the tractor's weight itself.

Question 3 · medium

A belt to a thresher runs at 12 m/s with tight-side tension 1200 N and slack-side tension 450 N. Ignoring centrifugal tension, what power does it transmit?

  1. 19.8 kW
  2. 9.0 kW
  3. 14.4 kW
  4. 62.5 kW
Answer and working

B. 9.0 kW

P = (T1 - T2) v = (1200 - 450) x 12 = 9000 W = 9.0 kW. Adding the tensions gives 19.8 kW; the effective driving force is the difference, because the slack side pulls back. 14.4 kW uses the tight-side tension alone (1200 x 12); 62.5 kW divides the tension difference by the speed.

Question 4 · hard

A flat belt and a V-belt (groove angle 40 degrees) have the same coefficient of friction 0.3 and 180 degrees of wrap. Which pair of limiting tension ratios is correct?

  1. Flat 2.57, V-belt 1.38
  2. Flat 2.57, V-belt 15.73
  3. Flat 2.57, V-belt 4.33
  4. Flat 2.83 x 10^23, V-belt 15.73
Answer and working

B. Flat 2.57, V-belt 15.73

Flat: e^(0.3 x pi) = 2.57. V-belt: e^(mu theta / sin beta), beta = half the groove angle = 20 degrees: e^(0.9425 / 0.342) = 15.73. Multiplying by sin beta or using the full 40 degrees understates the wedge effect; using 180 as radians gives an absurd number.

Question 5 · medium

On level wheel scales a tractor shows 11 kN on the front axle and 19 kN on the rear axle. The wheelbase is 2.2 m. How far ahead of the rear axle is its centre of gravity?

  1. 1.393 m
  2. 0.807 m
  3. 1.274 m
  4. 1.100 m
Answer and working

B. 0.807 m

Moments about the rear axle: W x = Rf L, so x = 11 x 2.2 / 30 = 0.807 m. 1.393 m is the distance from the front axle; dividing by the rear load instead of the total weight gives 1.274 m. 1.100 m simply halves the wheelbase.

Question 6 · medium

Why can the height of a tractor's centre of gravity not be found by weighing it on level ground?

  1. On level ground the tyres compress unevenly, so the axle loads measured are always unreliable
  2. On level ground the CG height has no moment arm about the axles, so axle loads do not depend on it
  3. On level ground the CG always lies at the axle height, so it is known without any weighing
  4. On level ground the scales read mass rather than weight, so the height cannot be resolved
Answer and working

B. On level ground the CG height has no moment arm about the axles, so axle loads do not depend on it

Weights act vertically, so the height of the CG does not enter the moment balance on level ground. Tilting the tractor, by raising one axle a known amount, gives the CG a horizontal shift that depends on its height, and the change in axle load reveals it.

Question 7 · hard

During a drawbar test, a tractor drive wheel of rolling radius 0.8 m turns at 25 rev/min while the tractor moves at 1.8 m/s. What is the wheel slip?

  1. 16.4 %
  2. 14.1 %
  3. -71.9 %
  4. 85.9 %
Answer and working

B. 14.1 %

Theoretical speed = 2 pi r N / 60 = 2 pi x 0.8 x 25 / 60 = 2.094 m/s. Slip = (1 - 1.8 / 2.094) x 100 = 14.1 %. Dividing by the actual speed gives 16.4 %; 85.9 % is the ratio of speeds, not the slip. -71.9 % takes 0.8 m as the wheel diameter, so the theoretical speed is only 1.047 m/s.

Question 8 · hard

In a rigid model of a vehicle turning on level ground, with track width b, centre-of-gravity height h and tyre-ground friction coefficient mu, the vehicle will skid sideways before it overturns if:

  1. mu is less than b / (2h)
  2. mu is greater than b / (2h)
  3. mu is less than 2h / b
  4. mu is equal to h / b
Answer and working

A. mu is less than b / (2h)

Sliding starts when m v^2/r = mu m g; overturning when m v^2/r = m g b/(2h). The lower threshold is reached first, so skidding comes first if mu < b/(2h). A low, wide vehicle on a slippery surface skids; a tall, narrow one on grippy ground tips.

Question 9 · medium

A PTO-driven pump absorbs a torque of 350 N m at the standard 540 rev/min. What power does it take from the PTO?

  1. 19.79 kW
  2. 189.0 kW
  3. 3.15 kW
  4. 1188 kW
Answer and working

A. 19.79 kW

P = T omega = 350 x (2 pi x 540 / 60) = 350 x 56.55 = 19792 W = 19.79 kW. Multiplying by rev/min gives 189 kW; dividing by 60 without 2 pi gives 3.15 kW. 1188 kW includes 2 pi but forgets to divide by 60.

Question 10 · hard

A thresher cylinder with a mass moment of inertia of 4 kg m2 slows from 1500 to 1400 rev/min while a wad of crop passes through. How much energy does it give up?

  1. 0.219 kJ
  2. 0.16 kJ
  3. 12.72 kJ
  4. 6.36 kJ
Answer and working

D. 6.36 kJ

omega1 = 157.08 rad/s, omega2 = 146.61 rad/s. Energy released = 0.5 I (omega1^2 - omega2^2) = 0.5 x 4 x (24674 - 21494) = 6360 J. Squaring the speed difference gives only 219 J; leaving out the 1/2 gives 12.72 kJ; using rev/min directly gives a huge 580,000 J. 0.16 kJ uses rev/s without 2 pi (0.5 x 4 x (25^2 - 23.33^2)).

A study plan for Engineering Mechanics (Statics & Dynamics) in GATE

This plan follows where our questions actually fall, so the time goes where the marks are likely to be. It is our reading of the syllabus, not the exam body's weighting.

  1. First, the heavy units (53% of the 17 questions): Free-body diagrams and equilibrium (3, 18%); Friction, including belt friction (3, 18%); Kinetics: Newton's laws and D'Alembert's principle (3, 18%).

    Read the manual chapters for these first and do every worked question you can find on them.

  2. Then the middle band: Work-energy principle (3, 18%); Centroid and centre of gravity (2, 12%); Area and mass moment of inertia (1, 6%).

    Aim for one sitting per unit, then mixed questions across them.

  3. Then the lighter units: Kinematics of particles and rigid bodies (1, 6%); Virtual work (1, 6%).

    Learn the definitions, classifications and standard numbers; these units are more often recalled than worked.

  4. Leave time for the hard ones: Kinetics: Newton's laws and D'Alembert's principle (3 hard of 3), Area and mass moment of inertia (1 hard of 1), Kinematics of particles and rigid bodies (1 hard of 1).

    Come back to these after a first pass, untimed, and read every explanation, including for the options you rejected.

  5. Finish timed. Sit the subject as a timed set without notes, mark it, and send each wrong answer back to its unit above.

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