Work, Energy and Power

• This section contains 20 multiple-choice questions, each with 4 options and only one correct answer

Marking Scheme

• +4 marks for each correct answer
• 0 marks if no option is selected
• -1 mark for each wrong answer

Question 1

• A spring obeys Hooke's law and is initially un-stretched, then an increasing force is applied, extending it by an amount x when force reaches magnitude Fm
• The work done in stretching the spring is 0.5 Fmx

Question 2

• The force acting on a particle is (2i + 3j) N
• The work done by this force is zero when the particle moves on the line 3y + kx = 5
• The value of k is 2.

Question 3

• A 2 kg object moves slowly from point A to point B on a curved path with a tangential force
• The coefficients of friction are µs = 0.3 and µk = 0.1, with g = 10 m/s²
• The work done by external force in moving the body is 400 J

Question 4

• A chain of mass m and length L is on a frictionless table with ¹/n hanging over the edge
• The work needed to pull the hanging part back on the table is mgL / 2n²

Question 5

• Force F = 8t (N/s) acts on a 2 kg body initially at rest on a smooth surface
• t is in seconds
• The work done by this force in the first 2 seconds, assuming constant force direction and movement, is 64 J.

Question 6

• The work done by the normal force exerted on each block by the bigger block is calculated for 1 second
• WA ≠ 0, WB ≠ 0, and WC ≠ 0 where A, B, and C are 1kg, 5kg, and 3kg blocks, respectively.

Question 7

• A student of mass M grabs a rope around a ceiling pulley as friends lift them a distance l
• The total work done on the student by all forces, including gravity, is zero, neglecting rope mass and friction

Question 8

• A body of mass m is slowly hauled up a hill by a force F tangent to the path
• The hill has height h, base length l, and friction coefficient µ
• The work done by force F is mgh + µmgl

Question 9

• Net force on a particle acts in the +x direction, increasing from 0 at x=0 to 24.0 N at x=3.0 m
• It is constant at 24.0 N from x=3.0 m to x=8.0 m, then decreases to 0 at x=13.0 m
• The work done to move the particle from x=0 to x=13.0 m is 212 J

Question 10

• A position-time graph of a 2 kg particle is provided for t = 0 to t = 4s
• The total work done on the particle is 0 J

Question 11

• Components of a force on a particle vary according to graphs
• The particle moves from A(0, 5, 12) to B(8, 20, 0) parallel to the x, y, then z axes
• The work done by this force is 250 J

Question 12

• A crate is initially at rest on a horizontal frictionless table
• A constant horizontal force F is applied
• The correct plot of work W as a function of the crate's speed v is graph D

Question 13

• A 40 N block travels down a smooth curved track AB, then onto a rough horizontal surface with a friction coefficient of 0.10
• Starting from a 2.0 m height, the distance it moves on the rough surface is 20 m.

Question 14

• A 2 kg sleeve at the origin moves on a parabolic wire x² = 4y, with forces F₁ (constant in x-direction) and F₂ (constant direction and magnitude)
• The net work done by F₁ and F₂ as the body moves from the origin to x=4 is 67.7 J

Question 15

• A particle moves from the origin in three equal distance spells along the x, y, and z axes
• A constant 50 N force acts along the direction of motion
• With equal work done in each spell and a total work of 300 J, the particle's final coordinates are (2, 2, 2) m

Question 16

• A special compression device exerts a force F = kx(x - l) for 0 < x < l, where l is max compression and k is constant
• The compression distance d maximizes work when d = l

Question 17

• A body moves slowly along paths ABC and ADC in a vertical plane
• ABC has a friction coefficient µ, ADC has 2µ, where µ = 1
• The ratio of work done by an external agent along ADC to ABC is 3:2

Question 18

• A force F = -k(xi + yj) acts on a particle moving in the x-y plane, where k is a positive constant
• Starting from the origin, the particle goes to (a, a) and then to (a/2, 0)
• The total work done by the force F on the particle is 3ka²/4

Question 19

• A block of mass m is hung from an elastic thread with force constant 2mg/a, initially at its natural length and allowed to fall freely
• The work done on the block by earth when it passes through the equilibrium position is mga / 2

Question 20

• A 30 N force acts along i + j + k, displacing a particle from (2, 4, 1) to (3, 5, 2)
• The work done during this displacement is 30√3 J

Integer Type Questions - Instructions

• Attempt any 5 out of the 10 questions
• If more than 5 questions are attempted, only the first 5 will be evaluated
• Answers are integer values, round off if needed
• Marking Scheme: +4 for correct, 0 if none selected, -1 for wrong answer

Question 1

• A mass 2m is on a smooth circular track of mass m on a smooth horizontal surface
• The circular track has a horizontal velocity √2gR towards left
• To find the maximum height reached by 2m in meters (R = 6 meters)
• The answer is 2

Question 2

• An observer and a vehicle start together, accelerating at 1 m/s² and 2 m/s² respectively
• A 1 kg block is on the vehicle floor, with a friction coefficient of 0.1
• The friction force's work on the 1kg block, observed by the running observer in the first second of the motion is 0 J

Question 3

• A 4 kg block rests on a 12 kg block accelerating at 5.2 m/s² on a smooth table with external force
• The friction coefficient is half the minimum needed to prevent slipping
• If the blocks slide, the amount of heat generated after the 12 kg block moves 10 m from rest is determined
• α/13 = 4

Question 4

• A 100 kg ladder descends at 3 m/s, while a 50 kg boy ascends at 5 m/s relative to the ladder
• The work done by gravity on the ladder and boy in 2 seconds are W₁ and W₂ respectively
• W₁ – W₂ = nkJ, n = 8

Question 5

• Force acting on a particle moving in a straight line depends on velocity as F = 2/v N
• The work done by this force in 3.5 seconds is 7 J

Question 6

• A 10g bullet has a velocity of 600 m/s upon exiting a rifle barrel
• If the barrel is 60cm long, the average force is α kN = 3

Question 7

• Four 4 kg packages are equally spaced (d = 200 mm)
• Initially, belt is at rest
• A constant 840 N force is applied
• The velocity of package 2 as it falls off the belt is 7 m/s

Question 8

• A force F = (3i + 7j - 5k) N acts on an object and displaces it from (1, 2, 3) to (4, -5, -6)
• The work done is 5J

Question 9

• A particle moves according to equations x = 10sin(2πt), y = 10cos(2πt)
• The work performed by the net force from t = 0 to t = 5 seconds is 0

Question 10

• A bead of mass m moves along an elliptical wire frame x = 2acosθ, y = asinθ in a horizontal plane
• A force F = (k/r²)r is applied to move the bead from point A to B
• The value of α in the equation for work done (αk/2a) is 1