Physics Syllabus (JEE Main)
Q. A damped oscillator has a time constant of 3 seconds. What is the damping coefficient if the mass is 1 kg and the spring constant is 4 N/m?
A.
1.5 kg/s
B.
2 kg/s
C.
3 kg/s
D.
4 kg/s
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Solution
Time constant (τ) = m/c, thus c = m/τ = 1/3 = 0.333 kg/s. Using c = 2ζ√(mk), we find ζ = 0.5.
Correct Answer: B — 2 kg/s
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Q. A diamond has a refractive index of 2.42. What is the critical angle for total internal reflection at the diamond-air interface?
A.
24.4°
B.
41.1°
C.
23.6°
D.
17.5°
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Solution
Critical angle θc = sin^(-1)(1/n) = sin^(-1)(1/2.42) ≈ 24.4°.
Correct Answer: A — 24.4°
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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
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Solution
The dipole moment p is defined as p = q * d.
Correct Answer: A — qd
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Q. A dipole consists of two charges +q and -q separated by a distance d. What is the dipole moment?
A.
qd
B.
q/d
C.
q^2d
D.
q/d^2
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Solution
The dipole moment p = q * d.
Correct Answer: A — qd
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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
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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
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Q. A dipole consists of two equal and opposite charges separated by a distance. What happens to the dipole moment if the distance is doubled?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
Dipole moment p = q * d, if d is doubled, p also doubles.
Correct Answer: A — It doubles
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Q. A dipole moment is defined as the product of charge and the distance between the charges. What is the dipole moment of a dipole consisting of charges +2μC and -2μC separated by 0.1m?
A.
4 × 10^-7 C m
B.
2 × 10^-7 C m
C.
2 × 10^-6 C m
D.
4 × 10^-6 C m
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Solution
Dipole moment p = q * d = (2 × 10^-6 C) * (0.1 m) = 2 × 10^-7 C m.
Correct Answer: A — 4 × 10^-7 C m
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Q. A dipole moment p is placed in a uniform electric field E. What is the torque experienced by the dipole?
A.
pE
B.
pE sin θ
C.
pE cos θ
D.
0
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Solution
Torque τ = p × E = pE sin θ, where θ is the angle between p and E.
Correct Answer: B — pE sin θ
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Q. A disc of mass M and radius R is rotating about its axis with an angular velocity ω. What is the angular momentum of the disc?
A.
(1/2)MR^2ω
B.
MR^2ω
C.
MRω
D.
(1/4)MR^2ω
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Solution
Angular momentum L = Iω, where I = (1/2)MR^2 for a disc.
Correct Answer: A — (1/2)MR^2ω
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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
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Solution
Kinetic energy K = (1/2)Iω^2, where I = (1/2)MR^2 for a disc.
Correct Answer: A — (1/2)Iω^2
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Q. A disc of radius R and mass M is rotating about its axis with an angular velocity ω. What is its kinetic energy?
A.
(1/2)Iω^2
B.
(1/2)Mω^2
C.
(1/2)M(R^2)ω^2
D.
(1/2)(MR^2)ω^2
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Solution
The moment of inertia I of a disc about its axis is (1/2)MR^2. Therefore, the kinetic energy K.E. = (1/2)Iω^2 = (1/2)(1/2)MR^2ω^2 = (1/4)MR^2ω^2.
Correct Answer: D — (1/2)(MR^2)ω^2
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Q. A disc rolls without slipping on a horizontal surface. If its radius is R and it rolls with a linear speed v, what is its angular speed?
A.
v/R
B.
2v/R
C.
v/2R
D.
v^2/R
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Solution
The relationship between linear speed and angular speed for rolling without slipping is ω = v/R.
Correct Answer: A — v/R
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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
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Solution
The disk has a lower moment of inertia compared to the ring, thus it reaches the ground first.
Correct Answer: A — Disk
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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
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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
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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
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Solution
The disk has a smaller moment of inertia compared to the ring, hence it will reach the bottom first.
Correct Answer: A — Disk
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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
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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
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Q. A disk and a ring of the same mass and radius are rolling without slipping. Which one will reach the bottom of an incline first?
A.
Disk
B.
Ring
C.
Both will reach at the same time
D.
Depends on the angle of incline
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Solution
The disk will reach the bottom first because it has a smaller moment of inertia compared to the ring.
Correct Answer: A — Disk
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Q. A disk is rotating with an angular velocity of 10 rad/s. If it experiences a constant angular acceleration of 2 rad/s², what will be its angular velocity after 5 seconds?
A.
20 rad/s
B.
10 rad/s
C.
30 rad/s
D.
15 rad/s
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Solution
Using the formula ω = ω₀ + αt, we have ω = 10 + 2*5 = 20 rad/s.
Correct Answer: A — 20 rad/s
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Q. A disk of radius R and mass M is rotating about its axis with an angular velocity ω. What is its angular momentum?
A.
(1/2)MR^2ω
B.
MR^2ω
C.
Mω
D.
(1/4)MR^2ω
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Solution
Angular momentum L = Iω, where I = (1/2)MR^2 for a disk.
Correct Answer: A — (1/2)MR^2ω
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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
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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
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Q. A disk of radius R and mass M is rotating about its axis with an angular velocity ω. What is its kinetic energy?
A.
(1/2)Mω^2R^2
B.
(1/2)Iω^2
C.
(1/2)Mω^2
D.
Mω^2R
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Solution
The moment of inertia I of a disk about its axis is (1/2)MR^2. Therefore, the kinetic energy K.E. = (1/2)Iω^2 = (1/2)(1/2)MR^2ω^2 = (1/4)MR^2ω^2.
Correct Answer: B — (1/2)Iω^2
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Q. A disk rolls down a slope of height h. What fraction of its total energy is translational at the bottom?
A.
1/3
B.
1/2
C.
2/3
D.
1
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Solution
At the bottom, the total energy is converted into translational and rotational energy. The translational energy is 2/3 of the total energy.
Correct Answer: C — 2/3
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Q. A disk rolls down a slope of height h. What is the ratio of translational to rotational kinetic energy at the bottom?
A.
1:1
B.
2:1
C.
3:1
D.
1:2
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Solution
At the bottom, the total kinetic energy is split equally between translational and rotational for a disk, hence the ratio is 1:1.
Correct Answer: A — 1:1
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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)
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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)
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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
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Solution
The relationship between linear speed and angular speed for rolling without slipping is given by ω = v/R.
Correct Answer: A — v/R
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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?
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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
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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)
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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
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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 conserve angular momentum?
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Solution
To conserve angular momentum, if the radius is doubled, the angular velocity must be halved.
Correct Answer: C — ω/2
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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?
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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
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Q. A disk rotates about its axis with an angular velocity of ω. If its radius is doubled while keeping the mass constant, what will be the new angular momentum?
A.
2Iω
B.
4Iω
C.
Iω
D.
I(2ω)
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Solution
The moment of inertia I of a disk is proportional to r^2, so if the radius is doubled, I becomes 4I. Thus, angular momentum L = Iω becomes 4Iω.
Correct Answer: B — 4Iω
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