GATE — Agricultural Engineering (AG) · India · IITs and IISc on rotation (2026: IIT Guwahati)
Original practice questions written to the published syllabus · not past papersHow mechanisms move and transmit power: linkages, cams, gears, belts, flywheels, governors, balancing and vibration.
In the exams: GATE AG Sections 2 and 3 (power transmission, belts and gears recur); ICAR AIEEA-PG Unit III
GATE — Agricultural Engineering (AG)
Numerical and NAT questions on belt drives (velocity ratio with slip, tension ratio, power, centrifugal tension), gear and planetary trains (tractor final drives, holding torque, efficiency per mesh), flywheel inertia from energy fluctuation or engine output, governor regulation, clutch torque and brake power. Mechanism mobility and Grashof checks appear as quick one-mark items.
How our questions for GATE spread across the units of Theory of Machines. Difficulty: 36 easy, 49 medium, 28 hard.
| Gears and gear trains: simple, compound and epicyclic | 15 | |
| Belt, rope and chain drives: tension ratio and power | 14 | |
| Free and forced vibrations and critical speed | 14 | |
| Flywheels and turning-moment diagrams | 11 | |
| Mechanisms, links, pairs and Grashof's law | 9 | |
| Velocity and acceleration analysis | 9 | |
| Clutches | 9 | |
| Governors | 8 | |
| Cams and followers | 7 | |
| Balancing of rotating and reciprocating masses | 7 | |
| Brakes and dynamometers | 6 | |
| Differential gear | 4 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
The Scotch yoke, which gives a slider exact simple harmonic motion, is an inversion of which kinematic chain?
C. The double slider-crank chain
The double slider-crank chain (two turning and two sliding pairs) gives the elliptical trammel, the Scotch yoke and the Oldham coupling. The single slider-crank chain has three turning pairs and one sliding pair and its slider motion is not exactly harmonic because of connecting-rod obliquity.
Further reading: Rattan, Theory of Machines
A belt running at 15 m/s has a tight-side tension of 1200 N and a slack-side tension of 450 N. What power does it transmit?
C. 11.25 kW
P = (T1 - T2)v = (1200 - 450) x 15 = 11 250 W = 11.25 kW. Adding the tensions gives 24.75 kW; T1 x v gives 18 kW; T2 x v gives 6.75 kW.
Further reading: Rattan, Theory of Machines
A 17-tooth sprocket on a roller chain of 15.875 mm pitch turns at 400 rpm. What is the average chain speed?
C. 1.80 m/s
Average chain speed v = pTN/60 = 0.015875 x 17 x 400/60 = 1.80 m/s: in one revolution T pitches of chain pass the sprocket. Forgetting to divide by 60 gives a per-minute figure; forgetting the tooth number gives one pitch per revolution; multiplying by 2π wrongly converts an already linear quantity.
Further reading: Rattan, Theory of Machines
What is the hoop stress in the thin rim of a cast-iron flywheel of density 7200 kg/m³ when the rim speed is 30 m/s?
D. 6.48 MPa
For a thin rotating rim σ = ρv² = 7200 x 900 = 6480000 Pa = 6.48 MPa, independent of the rim section. Using v instead of v² gives 0.216 MPa; multiplying by g treats density as a weight density. 3.24 MPa is half the correct value.
Further reading: Rattan, Theory of Machines
A solid disc flywheel of mass 100 kg and radius 0.4 m spins at 1200 rpm. How much kinetic energy does it store?
D. 63.2 kJ
I = mR²/2 = 100 x 0.16/2 = 8 kg m²; ω = 125.66 rad/s; E = ½Iω² = 0.5 x 8 x 15791 = 63.2 kJ. Treating the disc as a thin rim (I = mR²) doubles the answer; applying the ½ twice halves it; using rpm instead of rad/s gives 5760 kJ, and 5.8 kJ is that figure with the unit prefix slipped.
What condition must a centrifugal governor satisfy to be stable?
D. Radius must rise with speed
Stability means one equilibrium radius for each speed, which requires the controlling force to rise faster than proportionally with radius so that radius increases with speed. Equal speed at all radii is isochronism, the limit of stability; a central load (Porter) does not affect whether the governor is stable in this sense.
Further reading: Rattan, Theory of Machines
Two masses rotate in one plane: m1r1 = 0.6 kg m at 0° and m2r2 = 0.8 kg m at 90°. A single balancing mass is to be placed at 0.25 m radius. What mass is needed and at what angle?
B. 4.0 kg at 233.1°
Resultant mr = √(0.6² + 0.8²) = 1.0 kg m at tan⁻¹(0.8/0.6) = 53.1°. The balancing mass must supply equal and opposite mr: m = 1.0/0.25 = 4.0 kg at 53.1° + 180° = 233.1°. Placing it at 53.1° doubles the unbalance; adding mr arithmetically gives 5.6 kg.
Further reading: Rattan, Theory of Machines
A machine is mounted on springs to reduce the force transmitted to its foundation. For the transmitted force to be less than the exciting force, the ratio of forcing frequency to natural frequency must be:
C. greater than √2
Transmissibility falls below 1 only when ω/ωn > √2, whatever the damping. Below √2, and especially near r = 1 (resonance), the mounts amplify the force. Mounts therefore need to be soft enough to put the natural frequency well below the running frequency.
Further reading: Rao, Mechanical Vibrations
A clutch transmits 300 N m at 2000 rpm without slipping. What power does it transmit?
A. 62.8 kW
P = Tω = 300 x 2π x 2000/60 = 62832 W = 62.8 kW. Multiplying torque by rpm gives 600 kW; dividing the correct answer by 2 has no basis. 31.4 kW is half the correct value; 0.6 kW multiplies torque by rpm and divides by 10⁶.
Further reading: Rattan, Theory of Machines
A multi-plate clutch has 5 plates on the driving shaft and 4 plates on the driven shaft. How many pairs of friction surfaces transmit torque?
C. 8
Number of pairs of contact surfaces n = n1 + n2 - 1 = 5 + 4 - 1 = 8. Adding the plates without subtracting one gives 9; counting both faces of every plate gives 18 or 20.
Further reading: Rattan, Theory of Machines
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