Q. A copper wire has a resistivity of 1.68 x 10^-8 Ω·m. What is the resistance of a 100 m long wire with a cross-sectional area of 1 mm²?
A.1.68 Ω
B.0.168 Ω
C.0.0168 Ω
D.16.8 Ω
Solution
Resistance (R) = ρ * (L / A) = 1.68 x 10^-8 * (100 / 1 x 10^-6) = 1.68 Ω.
Correct Answer: A — 1.68 Ω
Q. A cube of side length a has a charge Q at one of its corners. What is the total electric flux through the cube?
A.Q/ε₀
B.Q/(6ε₀)
C.Q/(12ε₀)
D.0
Solution
The charge at one corner contributes 1/8 of its flux to the cube. Thus, total flux = (1/8)Q/ε₀ = Q/(12ε₀).
Correct Answer: C — Q/(12ε₀)
Q. A cyclist accelerates from rest at a rate of 1 m/s². How far will he travel in 10 seconds?
A.50 m
B.100 m
C.150 m
D.200 m
Solution
Using the formula: distance = initial velocity * time + 0.5 * acceleration * time². Distance = 0 + 0.5 * 1 * 10² = 50 m.
Correct Answer: B — 100 m
Q. A cyclist accelerates from rest at a rate of 2 m/s². How far will he travel in 10 seconds?
A.100 m
B.50 m
C.200 m
D.150 m
Solution
Using the formula: distance = ut + 0.5at². Here, u = 0, a = 2 m/s², t = 10 s. Distance = 0 + 0.5 * 2 * 10² = 100 m.
Correct Answer: A — 100 m
Q. A cyclist accelerates from rest to a speed of 10 m/s in 5 seconds. What is the average power output if the cyclist has a mass of 70 kg?
A.140 W
B.280 W
C.560 W
D.700 W
Solution
Kinetic Energy = 0.5 × m × v² = 0.5 × 70 kg × (10 m/s)² = 3500 J. Power = Work / Time = 3500 J / 5 s = 700 W.
Correct Answer: C — 560 W
Q. A cyclist accelerates from rest to a speed of 15 m/s. If the mass of the cyclist and the bicycle is 75 kg, what is the kinetic energy at that speed?
A.500 J
B.750 J
C.1000 J
D.1250 J
Solution
Kinetic Energy = 0.5 × mass × velocity² = 0.5 × 75 kg × (15 m/s)² = 8437.5 J.
Correct Answer: C — 1000 J
Q. A cyclist does 300 J of work to climb a hill. If the height of the hill is 5 m, what is the effective weight of the cyclist?
A.30 kg
B.60 kg
C.90 kg
D.120 kg
Solution
Weight = Work / Height = 300 J / 5 m = 60 N; mass = Weight / g = 60 N / 9.8 m/s² ≈ 6.12 kg.
Correct Answer: B — 60 kg
Q. A cyclist is moving around a circular track of radius 100 m. If he completes one lap in 40 seconds, what is his average speed?
A.5 m/s
B.10 m/s
C.15 m/s
D.20 m/s
Solution
Circumference = 2πr = 2π(100 m). Average speed = distance/time = (2π(100 m))/40 s ≈ 15.7 m/s.
Correct Answer: B — 10 m/s
Q. A cyclist is moving at 15 m/s and a pedestrian is walking at 5 m/s in the same direction. What is the relative speed of the pedestrian with respect to the cyclist?
A.10 m/s
B.5 m/s
C.20 m/s
D.15 m/s
Solution
Relative speed = Speed of pedestrian - Speed of cyclist = 5 m/s - 15 m/s = -10 m/s (10 m/s behind).
Correct Answer: A — 10 m/s
Q. A cyclist is moving at 15 m/s and passes a stationary observer. If the observer starts moving at 5 m/s in the same direction, what is the speed of the cyclist relative to the observer?
A.10 m/s
B.15 m/s
C.20 m/s
D.5 m/s
Solution
Relative speed = Speed of cyclist - Speed of observer = 15 m/s - 5 m/s = 10 m/s.
Correct Answer: A — 10 m/s
Q. A cyclist is moving at 15 m/s towards the east while a car is moving at 25 m/s towards the west. What is the relative speed of the cyclist with respect to the car?
A.10 m/s
B.15 m/s
C.40 m/s
D.25 m/s
Solution
Relative speed = Speed of cyclist + Speed of car = 15 m/s + 25 m/s = 40 m/s.
Correct Answer: C — 40 m/s
Q. A cyclist is moving at 15 m/s while a car is moving at 25 m/s in the same direction. What is the speed of the cyclist relative to the car?
A.10 m/s
B.15 m/s
C.25 m/s
D.40 m/s
Solution
Relative speed = Speed of car - Speed of cyclist = 25 m/s - 15 m/s = 10 m/s.
Correct Answer: A — 10 m/s
Q. A cyclist is moving in a circular track of radius 30 m with a speed of 15 m/s. What is the net force acting on the cyclist if the mass of the cyclist is 60 kg?
A.180 N
B.120 N
C.90 N
D.60 N
Solution
Centripetal force F = mv²/r = 60 kg * (15 m/s)² / 30 m = 180 N.
Correct Answer: A — 180 N
Q. A cyclist is moving in a circular track of radius 30 m. If he completes one round in 12 seconds, what is his average speed?
A.5 m/s
B.10 m/s
C.15 m/s
D.20 m/s
Solution
Circumference = 2πr = 2π(30) = 60π m. Average speed = distance/time = 60π m / 12 s = 5 m/s.
Correct Answer: B — 10 m/s
Q. A cyclist is moving in a circular track of radius 30 m. If the cyclist completes one round in 12 seconds, what is the average speed of the cyclist?
A.5 m/s
B.10 m/s
C.15 m/s
D.20 m/s
Solution
Circumference = 2πr = 2π(30 m). Average speed = distance/time = (2π(30 m))/12 s ≈ 5 m/s.
Correct Answer: B — 10 m/s
Q. A cyclist is moving in a circular track of radius 30 m. If the cyclist completes one round in 12 seconds, what is the angular velocity of the cyclist?
A.π/6 rad/s
B.π/3 rad/s
C.2π/6 rad/s
D.2π/3 rad/s
Solution
Angular velocity (ω) = 2π/T = 2π/12 = π/6 rad/s.
Correct Answer: B — π/3 rad/s
Q. A cyclist is negotiating a circular track of radius 30 m. If the cyclist's speed is 15 m/s, what is the net force acting on the cyclist towards the center of the track?
A.50 N
B.75 N
C.100 N
D.125 N
Solution
Centripetal force (F_c) = mv²/r. Assuming mass m = 100 kg, F_c = (100 kg)(15 m/s)² / (30 m) = 75 N.
Correct Answer: C — 100 N
Q. A cyclist travels 100 m in 5 seconds. What is the average speed of the cyclist?
A.10 m/s
B.15 m/s
C.20 m/s
D.25 m/s
Solution
Average speed = total distance / total time = 100 m / 5 s = 20 m/s.
Correct Answer: A — 10 m/s
Q. A cyclist travels 100 m north and then 100 m east. What is the magnitude of the displacement from the starting point?
A.100 m
B.141.4 m
C.200 m
D.50 m
Solution
Displacement = √(100² + 100²) = √20000 = 141.4 m.
Correct Answer: B — 141.4 m
Q. A cylinder rolls down a hill. If it has a radius R and rolls without slipping, what is the relationship between its linear velocity v and its angular velocity ω?
A.v = Rω
B.v = 2Rω
C.v = ω/R
D.v = R^2ω
Solution
For rolling without slipping, the relationship is v = Rω.
Correct Answer: A — v = Rω
Q. A cylinder rolls down a hill. If the height of the hill is h, what is the speed of the center of mass of the cylinder at the bottom of the hill?
A.√(gh)
B.√(2gh)
C.√(3gh)
D.√(4gh)
Solution
Using conservation of energy, potential energy at the top (mgh) converts to kinetic energy (1/2 mv^2 + 1/2 Iω^2). For a solid cylinder, I = 1/2 mr^2, leading to v = √(2gh).
Correct Answer: B — √(2gh)
Q. A cylindrical conductor has a length L and radius r. If the radius is doubled while keeping the length constant, how does the resistivity change?
A.Doubles
B.Halves
C.Remains the same
D.Increases four times
Solution
Resistivity is an intrinsic property of the material and does not change with geometry.
Correct Answer: C — Remains the same
Q. A cylindrical Gaussian surface encloses a charge Q. If the height of the cylinder is doubled while keeping the radius constant, what happens to the electric flux through the curved surface?
A.It doubles
B.It halves
C.It remains the same
D.It becomes zero
Solution
The electric flux through the curved surface is proportional to the charge enclosed, which remains constant, so the flux through the curved surface doubles if the height is doubled.
Correct Answer: A — It doubles
Q. A cylindrical Gaussian surface encloses a long straight wire carrying a current. What is the electric field at a point outside the cylinder?
A.Zero
B.Directly proportional to the distance from the wire
C.Inversely proportional to the distance from the wire
D.Constant
Solution
The electric field outside the cylindrical surface is directly proportional to the distance from the wire.
Correct Answer: B — Directly proportional to the distance from the wire
Q. A cylindrical Gaussian surface encloses a long straight wire carrying a current. What is the electric field at a distance r from the wire?
A.0
B.I/(2πε₀r)
C.λ/(2πε₀r)
D.σ/(2ε₀)
Solution
Gauss's law applies to electric fields, not magnetic fields. The electric field around a current-carrying wire is not defined by Gauss's law.
Correct Answer: A — 0
Q. A cylindrical Gaussian surface of length L and radius R encloses a charge Q. What is the electric field E at a distance R from the axis of the cylinder?
A.Q/(2πε₀R)
B.Q/(4πε₀R²)
C.Q/(ε₀L)
D.0
Solution
Using Gauss's law, the electric field E at a distance R from the axis of a long charged cylinder is E = Q/(2πε₀L) for points outside the cylinder.
Correct Answer: A — Q/(2πε₀R)
Q. A cylindrical rod is subjected to a tensile force. If the diameter of the rod is doubled while keeping the length constant, what happens to the stress in the rod?
A.Increases
B.Decreases
C.Remains the same
D.Becomes zero
Solution
Stress is defined as force per unit area. Doubling the diameter increases the area by a factor of four, thus reducing the stress.
Correct Answer: B — Decreases
Q. A cylindrical rod is subjected to a tensile force. If the radius of the rod is halved while keeping the length constant, how does the tensile stress change?
A.It doubles
B.It halves
C.It quadruples
D.It remains the same
Solution
Tensile stress is given by force/area. Halving the radius reduces the area by a factor of four, thus the stress quadruples for the same force.
Correct Answer: C — It quadruples
Q. A cylindrical wire has a length of 1 m and a radius of 0.5 mm. If its resistivity is 1.68 x 10^-8 Ω·m, what is its resistance?
A.0.0212 Ω
B.0.0424 Ω
C.0.0848 Ω
D.0.168 Ω
Solution
Resistance R = ρ(L/A) = 1.68 x 10^-8 * (1 / (π(0.5 x 10^-3)²)) = 0.0424 Ω.
Correct Answer: B — 0.0424 Ω
Q. A dipole consists of two charges +q and -q separated by a distance d. What is the expression for the dipole moment?
