Q. A die is rolled. What is the probability of rolling an even number given that the number rolled is greater than 2?
A.1/2
B.1/3
C.1/4
D.2/3
Solution
The possible outcomes greater than 2 are {3, 4, 5, 6}. The even numbers among these are {4, 6}. Thus, the probability is 2/3.
Correct Answer: D — 2/3
Q. A dipole consists of two charges +q and -q separated by a distance d. What is the expression for the dipole moment?
A.qd
B.q/d
C.q^2d
D.q/d^2
Solution
The dipole moment p is defined as p = q * d.
Correct Answer: A — qd
Q. A dipole consists of two equal and opposite charges separated by a distance of 0.1m. What is the dipole moment if each charge is 1μC?
A.1 × 10^-7 C m
B.1 × 10^-6 C m
C.1 × 10^-5 C m
D.1 × 10^-4 C m
Solution
Dipole moment p = q * d = (1 × 10^-6 C) * (0.1 m) = 1 × 10^-7 C m.
Correct Answer: B — 1 × 10^-6 C m
Q. A disc of radius R and mass M is rotating about its axis with an angular velocity ω. What is the kinetic energy of the disc?
A.(1/2)Iω^2
B.(1/2)Mω^2
C.Iω
D.Mω^2
Solution
Kinetic energy K = (1/2)Iω^2, where I = (1/2)MR^2 for a disc.
Correct Answer: A — (1/2)Iω^2
Q. A disk and a ring of the same mass and radius are released from rest at the same height. Which one reaches the ground first?
A.Disk
B.Ring
C.Both reach at the same time
D.Depends on the surface
Solution
The disk has a lower moment of inertia compared to the ring, thus it reaches the ground first.
Correct Answer: A — Disk
Q. A disk and a ring of the same mass and radius are rolling down an incline. Which will reach the bottom first?
A.Disk
B.Ring
C.Both will reach at the same time
D.Depends on the angle of incline
Solution
The disk has a smaller moment of inertia compared to the ring, hence it will reach the bottom first.
Correct Answer: A — Disk
Q. A disk and a ring of the same mass and radius are rolling down an incline. Which one will have a greater translational speed at the bottom?
A.Disk
B.Ring
C.Both have the same speed
D.Cannot be determined
Solution
The disk has a lower moment of inertia than the ring, allowing it to convert more potential energy into translational kinetic energy.
Correct Answer: A — Disk
Q. A disk and a ring of the same mass and radius are rolling without slipping down an incline. Which one will have a greater translational speed at the bottom?
A.Disk
B.Ring
C.Both have the same speed
D.Depends on the incline
Solution
The disk has a lower moment of inertia than the ring, allowing it to convert more potential energy into translational kinetic energy.
Correct Answer: A — Disk
Q. A disk of radius R and mass M is rotating about its axis with an angular velocity ω. What is the angular momentum of the disk?
A.(1/2)MR^2ω
B.MR^2ω
C.(1/4)MR^2ω
D.(3/2)MR^2ω
Solution
Angular momentum L = Iω = (1/2)MR^2ω, where I = (1/2)MR^2 for a disk.
Correct Answer: A — (1/2)MR^2ω
Q. A disk rolls down an incline. If the height of the incline is h, what is the speed of the disk at the bottom assuming no energy losses?
A.√(gh)
B.√(2gh)
C.√(3gh)
D.√(4gh)
Solution
Using conservation of energy, potential energy at height h converts to kinetic energy at the bottom. The speed is √(2gh).
Correct Answer: B — √(2gh)
Q. A disk rolls without slipping on a horizontal surface. If its radius is R and it rolls with a linear speed v, what is the angular speed of the disk?
A.v/R
B.R/v
C.vR
D.v^2/R
Solution
The relationship between linear speed and angular speed for rolling without slipping is given by ω = v/R.
Correct Answer: A — v/R
Q. A disk rotates about its axis with an angular velocity of ω. If its radius is doubled, what will be the new angular momentum?
A.2Iω
B.4Iω
C.Iω
D.I(2ω)
Solution
Angular momentum L = Iω, and if the radius is doubled, the moment of inertia I becomes 4I, thus L = 4Iω.
Correct Answer: B — 4Iω
Q. A disk rotates about its axis with an angular velocity of ω. If its radius is doubled, what will be the new angular velocity to maintain the same linear velocity at the edge?
A.ω/2
B.ω
C.2ω
D.4ω
Solution
The linear velocity v = rω. If the radius is doubled, to maintain the same v, the angular velocity must remain ω.
Correct Answer: B — ω
Q. A disk rotates about its axis with an angular velocity of ω. If its radius is doubled, what will be the new angular momentum if the mass remains the same?
A.2ω
B.4ω
C.ω
D.ω/2
Solution
Angular momentum L = Iω. If the radius is doubled, the moment of inertia increases by a factor of 4, thus L = 4Iω.
Correct Answer: B — 4ω
Q. A door is pushed at its edge with a force of 20 N. If the width of the door is 0.8 m, what is the torque about the hinges?
A.8 Nm
B.10 Nm
C.16 Nm
D.20 Nm
Solution
Torque (τ) = Force (F) × Distance (r) = 20 N × 0.8 m = 16 Nm.
Correct Answer: C — 16 Nm
Q. A door is pushed at its edge with a force of 20 N. If the width of the door is 1 m, what is the torque about the hinges?
A.10 Nm
B.20 Nm
C.30 Nm
D.40 Nm
Solution
Torque (τ) = F × d = 20 N × 1 m = 20 Nm.
Correct Answer: B — 20 Nm
Q. A door is pushed at its edge with a force of 50 N. If the width of the door is 1 m, what is the torque about the hinges?
A.25 Nm
B.50 Nm
C.75 Nm
D.100 Nm
Solution
Torque (τ) = Force (F) × Distance (r) = 50 N × 1 m = 50 Nm.
Correct Answer: B — 50 Nm
Q. A drop of liquid is in equilibrium on a surface. What is the condition for the drop to remain in equilibrium?
A.Weight equals surface tension
B.Weight equals gravitational force
C.Surface tension equals gravitational force
D.Surface tension equals buoyant force
Solution
For a drop to remain in equilibrium, the upward force due to surface tension must balance the downward gravitational force.
Correct Answer: C — Surface tension equals gravitational force
Q. A family has 2 children. What is the probability that both children are boys if it is known that at least one is a boy?
A.1/2
B.1/3
C.1/4
D.1/5
Solution
The possible combinations of children are BB, BG, GB, GG. Given that at least one is a boy, we can eliminate GG, leaving us with BB, BG, GB. Out of these 3 combinations, only 1 is BB. Therefore, the probability is 1/3.
Correct Answer: B — 1/3
Q. A family has 2 children. What is the probability that both children are boys, given that at least one is a boy?
A.1/3
B.1/2
C.1/4
D.2/3
Solution
The possible combinations are BB, BG, GB. Given at least one is a boy, the combinations are BB, BG, GB. The probability of both being boys is 1/3.
Correct Answer: A — 1/3
Q. A family has 2 children. What is the probability that both children are boys?
A.1/4
B.1/2
C.1/3
D.1/5
Solution
The possible combinations of children are BB, BG, GB, GG. Out of these, only 1 combination is both boys (BB). Thus, the probability is 1/4.
Correct Answer: A — 1/4
Q. A family has 3 children. What is the probability that at least one child is a girl given that at least one child is a boy?
A.1/2
B.2/3
C.3/4
D.1/4
Solution
The only combinations with at least one boy are: BBB, BBG, BGB, GBB, BGG, GBG, GGB. Out of these, all combinations except BBB have at least one girl. Thus, P(At least one girl | At least one boy) = 6/7.
Correct Answer: B — 2/3
Q. A fiber optic cable uses total internal reflection to transmit light. What is the primary requirement for this to work effectively?
A.The core must have a higher refractive index than the cladding
B.The cladding must have a higher refractive index than the core
C.The light must be monochromatic
D.The cable must be straight
Solution
For total internal reflection to occur in a fiber optic cable, the core must have a higher refractive index than the cladding.
Correct Answer: A — The core must have a higher refractive index than the cladding
Q. A fiber optic cable uses total internal reflection. What is the role of the cladding?
A.To increase the refractive index.
B.To decrease the refractive index.
C.To prevent light loss.
D.To enhance light absorption.
Solution
The cladding has a lower refractive index than the core, ensuring that light is kept within the core through total internal reflection.
Correct Answer: C — To prevent light loss.
Q. A figure skater spins with arms extended. When she pulls her arms in, what happens to her angular velocity?
A.Increases
B.Decreases
C.Remains the same
D.Becomes zero
Solution
By conservation of angular momentum, pulling arms in decreases moment of inertia, thus increasing angular velocity.
Correct Answer: A — Increases
Q. A figure skater spins with arms extended. When she pulls her arms in, what happens to her angular momentum?
A.Increases
B.Decreases
C.Remains the same
D.Becomes zero
Solution
Angular momentum remains the same; however, her angular velocity increases due to a decrease in moment of inertia.
Correct Answer: C — Remains the same
Q. A figure skater spins with arms extended. When she pulls her arms in, what happens to her rotational speed?
A.Increases
B.Decreases
C.Remains the same
D.Becomes zero
Solution
Pulling her arms in decreases her moment of inertia, causing her rotational speed to increase to conserve angular momentum.
Correct Answer: A — Increases
Q. A fluid with a viscosity of 0.1 Pa·s flows through a pipe of radius 0.05 m. If the pressure difference across the pipe is 1000 Pa, what is the flow rate?
A.0.01 m³/s
B.0.02 m³/s
C.0.03 m³/s
D.0.04 m³/s
Solution
Using Poiseuille's law, the flow rate Q = (π * r^4 * ΔP) / (8 * η * L). Assuming L = 1 m, Q = (π * (0.05)^4 * 1000) / (8 * 0.1 * 1) = 0.01 m³/s.
Correct Answer: A — 0.01 m³/s
Q. A flywheel is rotating with an angular speed of 20 rad/s. If it comes to rest in 5 seconds, what is the angular deceleration?
