Q. What is the minimum thickness of a soap bubble that will appear black in reflected light?
A.
λ/4
B.
λ/2
C.
λ
D.
3λ/4
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Solution
A soap bubble appears black in reflected light when the thickness is λ/4, leading to destructive interference.
Correct Answer: A — λ/4
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Q. What is the minimum thickness of a soap bubble that will appear black when viewed in white light?
A.
λ/4
B.
λ/2
C.
λ
D.
3λ/4
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Solution
A soap bubble appears black when the thickness is λ/4 due to destructive interference of light reflected from the top and bottom surfaces.
Correct Answer: A — λ/4
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Q. What is the minimum thickness of a soap film that appears dark in reflected light for a wavelength of 600 nm?
A.
150 nm
B.
300 nm
C.
600 nm
D.
1200 nm
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Solution
For destructive interference in reflected light, the minimum thickness t = λ/2n, where n is the refractive index (approximately 1.5 for soap). Thus, t = 600 nm / (2 * 1.5) = 200 nm.
Correct Answer: B — 300 nm
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Q. What is the minimum thickness of a soap film that appears dark when illuminated by white light?
A.
λ/4
B.
λ/2
C.
λ
D.
3λ/4
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Solution
For destructive interference in a soap film, the minimum thickness should be λ/2, considering the phase change upon reflection.
Correct Answer: B — λ/2
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Q. What is the minimum thickness of a soap film that appears dark when viewed in reflected light?
A.
λ/4
B.
λ/2
C.
λ
D.
3λ/4
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Solution
For destructive interference in reflected light, the minimum thickness of the film must be λ/2.
Correct Answer: B — λ/2
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Q. What is the mode of heat transfer that occurs through a fluid due to density differences?
A.
Conduction
B.
Convection
C.
Radiation
D.
Insulation
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Solution
Convection is the mode of heat transfer that occurs through a fluid due to density differences.
Correct Answer: B — Convection
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Q. What is the mode of heat transfer that occurs through a fluid without any movement of the fluid itself?
A.
Conduction
B.
Convection
C.
Radiation
D.
Diffusion
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Solution
Conduction is the mode of heat transfer that occurs through a solid or stationary fluid without any movement of the fluid itself.
Correct Answer: A — Conduction
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Q. What is the moment of inertia of a disk of mass M and radius R about an axis through its center and perpendicular to its plane?
A.
1/2 MR^2
B.
MR^2
C.
1/4 MR^2
D.
2/3 MR^2
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Solution
The moment of inertia of a disk about an axis through its center is I = 1/2 MR^2.
Correct Answer: A — 1/2 MR^2
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Q. What is the moment of inertia of a solid cylinder of mass M and radius R about its central axis?
A.
1/2 MR^2
B.
1/3 MR^2
C.
MR^2
D.
2/5 MR^2
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Solution
The moment of inertia of a solid cylinder about its central axis is given by I = 1/2 MR^2.
Correct Answer: A — 1/2 MR^2
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Q. What is the moment of inertia of a solid disk about its central axis?
A.
(1/2)MR^2
B.
(1/3)MR^2
C.
(1/4)MR^2
D.
MR^2
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Solution
The moment of inertia of a solid disk about its central axis is (1/2)MR^2.
Correct Answer: A — (1/2)MR^2
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Q. What is the moment of inertia of a solid sphere about an axis through its center?
A.
(2/5)mr^2
B.
(1/2)mr^2
C.
(1/3)mr^2
D.
(5/2)mr^2
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Solution
The moment of inertia of a solid sphere about an axis through its center is given by I = (2/5)mr^2.
Correct Answer: A — (2/5)mr^2
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Q. What is the moment of inertia of a solid sphere of mass M and radius R about an axis through its center?
A.
2/5 MR^2
B.
3/5 MR^2
C.
1/2 MR^2
D.
MR^2
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Solution
The moment of inertia of a solid sphere about an axis through its center is I = 2/5 MR^2.
Correct Answer: A — 2/5 MR^2
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Q. What is the moment of inertia of a thin circular hoop of mass M and radius R about an axis through its center?
A.
MR^2
B.
1/2 MR^2
C.
1/3 MR^2
D.
2/5 MR^2
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Solution
The moment of inertia of a thin circular hoop about an axis through its center is I = MR^2.
Correct Answer: A — MR^2
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Q. What is the moment of inertia of a thin circular plate of mass M and radius R about an axis through its center and perpendicular to its plane?
A.
1/2 MR^2
B.
MR^2
C.
1/4 MR^2
D.
1/3 MR^2
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Solution
The moment of inertia of a thin circular plate about an axis through its center is I = 1/2 MR^2.
Correct Answer: A — 1/2 MR^2
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Q. What is the moment of inertia of a thin circular ring of mass M and radius R about an axis perpendicular to its plane through its center?
A.
MR^2
B.
1/2 MR^2
C.
1/3 MR^2
D.
2/5 MR^2
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Solution
The moment of inertia of a thin circular ring about an axis through its center is I = MR^2.
Correct Answer: A — MR^2
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Q. What is the moment of inertia of a thin circular ring of mass M and radius R about an axis through its center?
A.
MR^2
B.
1/2 MR^2
C.
1/3 MR^2
D.
2/5 MR^2
Show solution
Solution
The moment of inertia of a thin circular ring about an axis through its center is I = MR^2.
Correct Answer: A — MR^2
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Q. What is the moment of inertia of a thin circular ring of mass M and radius R about an axis through its center and perpendicular to its plane?
A.
MR^2
B.
1/2 MR^2
C.
2/3 MR^2
D.
1/3 MR^2
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Solution
The moment of inertia of a thin circular ring about an axis through its center is I = MR^2.
Correct Answer: A — MR^2
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Q. What is the moment of inertia of a thin circular ring of mass M and radius R about an axis perpendicular to its plane and passing through its center?
A.
MR^2
B.
1/2 MR^2
C.
1/3 MR^2
D.
2/5 MR^2
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Solution
The moment of inertia of a thin circular ring about an axis through its center is I = MR^2.
Correct Answer: A — MR^2
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Q. What is the moment of inertia of a thin rod of length L about an axis perpendicular to it and passing through its center?
A.
(1/3)ML^2
B.
(1/12)ML^2
C.
(1/2)ML^2
D.
ML^2
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Solution
The moment of inertia of a thin rod about an axis through its center is given by I = (1/12)ML^2.
Correct Answer: B — (1/12)ML^2
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Q. What is the moment of inertia of a thin rod of length L about an axis perpendicular to it and passing through one end?
A.
(1/3)ML^2
B.
(1/12)ML^2
C.
ML^2
D.
(1/2)ML^2
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Solution
The moment of inertia of a thin rod about an end is given by I = (1/3)ML^2.
Correct Answer: A — (1/3)ML^2
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Q. What is the moment of inertia of a thin spherical shell of mass M and radius R about an axis through its center?
A.
2/3 MR^2
B.
1/2 MR^2
C.
MR^2
D.
2 MR^2
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Solution
The moment of inertia of a thin spherical shell about an axis through its center is I = 2/3 MR^2.
Correct Answer: A — 2/3 MR^2
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Q. What is the moment of inertia of a thin wire bent in the shape of a semicircle of radius R and mass M about the diameter?
A.
1/2 MR^2
B.
1/4 MR^2
C.
MR^2
D.
3/8 MR^2
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Solution
The moment of inertia of a thin wire bent in the shape of a semicircle about the diameter is I = 3/8 MR^2.
Correct Answer: D — 3/8 MR^2
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Q. What is the moment of inertia of a uniform rectangular plate of mass M and dimensions a x b about an axis through its center and parallel to side a?
A.
1/12 Ma^2
B.
1/12 Mb^2
C.
1/3 Ma^2
D.
1/3 Mb^2
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Solution
The moment of inertia of a rectangular plate about an axis through its center and parallel to side a is I = 1/3 Mb^2.
Correct Answer: D — 1/3 Mb^2
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Q. What is the moment of inertia of a uniform thin circular plate of mass M and radius R about an axis through its center and perpendicular to its plane?
A.
1/2 MR^2
B.
MR^2
C.
1/4 MR^2
D.
2/5 MR^2
Show solution
Solution
The moment of inertia of a uniform thin circular plate about an axis through its center and perpendicular to its plane is I = 1/2 MR^2.
Correct Answer: A — 1/2 MR^2
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Q. What is the moment of inertia of a uniform thin square plate of mass M and side length a about an axis through its center and parallel to one of its sides?
A.
1/6 Ma²
B.
1/12 Ma²
C.
1/4 Ma²
D.
1/3 Ma²
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Solution
The moment of inertia of a square plate about an axis through its center and parallel to one side is I = 1/12 Ma².
Correct Answer: B — 1/12 Ma²
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Q. What is the moment of inertia of a uniform triangular lamina of mass M and base b about an axis perpendicular to the base and passing through its centroid?
A.
1/18 Mb^2
B.
1/12 Mb^2
C.
1/6 Mb^2
D.
1/24 Mb^2
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Solution
The moment of inertia of a triangular lamina about an axis through its centroid is I = 1/12 Mb^2.
Correct Answer: B — 1/12 Mb^2
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Q. What is the nature of the image formed by a concave lens when the object is placed at infinity?
A.
Real and inverted
B.
Virtual and upright
C.
Real and upright
D.
Virtual and inverted
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Solution
A concave lens always produces a virtual and upright image regardless of the object's position.
Correct Answer: B — Virtual and upright
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Q. What is the nature of the image formed by a concave lens?
A.
Real and inverted
B.
Real and upright
C.
Virtual and upright
D.
Virtual and inverted
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Solution
A concave lens always forms a virtual and upright image.
Correct Answer: C — Virtual and upright
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Q. What is the nature of the image formed by a concave mirror when the object is placed beyond the center of curvature?
A.
Real and inverted
B.
Virtual and upright
C.
Real and upright
D.
Virtual and inverted
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Solution
When the object is beyond the center of curvature, the image formed is real and inverted.
Correct Answer: A — Real and inverted
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Q. What is the nature of the image formed by a convex lens when the object is placed beyond the focal length?
A.
Virtual and erect
B.
Real and inverted
C.
Real and erect
D.
Virtual and inverted
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Solution
When an object is placed beyond the focal length of a convex lens, the image formed is real and inverted.
Correct Answer: B — Real and inverted
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