JEE Advanced → IIT Kharagpur B.Tech Agricultural & Food Engineering · India · IITs (JoSAA counselling)
Original practice questions written to the published syllabus · not past papersForces, equilibrium and motion of particles and rigid bodies: the starting point for structures, machines and tractor mechanics.
In the exams: NCEES FE Statics 9–14 and Dynamics 9–14 questions; ICAR AIEEA-PG Unit IV
How our questions for JEE Advanced → IIT Kharagpur B.Tech Agricultural & Food Engineering spread across the units of Engineering Mechanics (Statics & Dynamics). Difficulty: 14 easy, 6 medium, 2 hard.
| Kinematics of particles and rigid bodies | 4 | |
| Kinetics: Newton's laws and D'Alembert's principle | 3 | |
| Force systems and resultants | 2 | |
| Friction, including belt friction | 2 | |
| Centroid and centre of gravity | 2 | |
| Area and mass moment of inertia | 2 | |
| Work-energy principle | 2 | |
| Impulse and momentum | 2 | |
| Virtual work | 2 | |
| Free-body diagrams and equilibrium | 1 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
A 1000 N sack hangs from a ring held by two ropes. One rope makes 60 degrees with the horizontal and the other 30 degrees with the horizontal, on opposite sides. Using Lami's theorem, what is the tension in the rope at 60 degrees to the horizontal?
D. 866 N
The three forces meet at the ring. The angle between the two ropes is 90 degrees, between the 30-degree rope and the vertical weight 120 degrees, and between the 60-degree rope and the weight 150 degrees. Lami: T60 / sin 120 = W / sin 90, so T60 = 1000 x 0.866 = 866 N; similarly T30 = 500 N. The steeper rope carries more load; giving it 500 N swaps the ropes. 577 N assumes the two ropes share the load equally (2T sin 60 = 1000).
Further reading: Meriam and Kraige, Engineering Mechanics: Statics / Dynamics
Spray droplets fall vertically at 3 m/s in still air while the sprayer moves forward at 4 m/s. What is the speed of the droplets relative to the sprayer?
A. 5.0 m/s
v(drop relative to sprayer) = v(drop) - v(sprayer). The two are perpendicular, so the magnitude is sqrt(3^2 + 4^2) = 5.0 m/s, angled backward. Adding or subtracting the speeds treats them as parallel. 2.65 m/s subtracts the squares (sqrt(16 - 9)).
Further reading: Meriam and Kraige, Engineering Mechanics: Statics / Dynamics
A hoist lifts a 400 kg pallet of feed with an upward acceleration of 1.5 m/s2. What is the tension in the hoist rope?
D. 4524 N
T - m g = m a, so T = m (g + a) = 400 x (9.81 + 1.5) = 4524 N. m (g - a) applies when accelerating downward; 3924 N is the static tension; m a alone forgets gravity.
Further reading: Meriam and Kraige, Engineering Mechanics: Statics / Dynamics
A trailer starts from rest and rolls freely down a ramp, dropping 2 m in height. Ignoring friction and wheel rotational inertia, what is its speed at the bottom?
D. 6.26 m/s
Energy conservation: m g h = 0.5 m v^2, v = sqrt(2 g h) = sqrt(2 x 9.81 x 2) = 6.26 m/s. The result is independent of mass and of the ramp shape. Omitting the square root gives 39.24. 4.43 m/s drops the 2 (sqrt(g h)); 19.62 is g h itself.
Further reading: Meriam and Kraige, Engineering Mechanics: Statics / Dynamics
In which kind of collision between two bodies is total kinetic energy conserved as well as total momentum?
A. A perfectly elastic collision, with coefficient of restitution equal to 1
Momentum is conserved whenever external impulse is negligible. Kinetic energy is conserved only if e = 1. With no external force momentum is conserved, but KE may still be lost to deformation and heat.
Further reading: Meriam and Kraige, Engineering Mechanics: Statics / Dynamics
A pulley block lifting an engine has four rope segments supporting the moving block. Ignoring friction and pulley weight, what pull on the free end holds a 2000 N load?
D. 500 N
Virtual work: raising the load by delta y shortens four supporting segments, so the free end moves 4 delta y. P x 4 delta y = 2000 x delta y, P = 500 N. Counting only two segments gives 1000 N. 8000 N multiplies by four instead of dividing.
Further reading: Meriam and Kraige, Engineering Mechanics: Statics / Dynamics
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