Q. If a torque of 25 Nm is applied to a wheel with a radius of 0.5 m, what is the force applied at the edge of the wheel?
A.
50 N
B.
40 N
C.
30 N
D.
20 N
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Solution
Force = Torque / Radius = 25 Nm / 0.5 m = 50 N.
Correct Answer: A — 50 N
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Q. If a torque of 25 Nm is generated by a force acting at a distance of 0.5 m, what is the force applied?
A.
50 N
B.
40 N
C.
30 N
D.
20 N
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Solution
Force = Torque / Distance = 25 Nm / 0.5 m = 50 N.
Correct Answer: A — 50 N
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Q. If a torque of 30 Nm is applied to a lever arm of 3 m, what is the force applied?
A.
5 N
B.
10 N
C.
15 N
D.
20 N
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Solution
Force = Torque / Distance = 30 Nm / 3 m = 10 N.
Correct Answer: B — 10 N
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Q. If a torque of 5 Nm is applied to a rotating object with a moment of inertia of 2 kg·m², what is the angular acceleration?
A.
2.5 rad/s²
B.
5 rad/s²
C.
10 rad/s²
D.
1 rad/s²
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Solution
Angular acceleration α = Torque / Moment of inertia = 5 Nm / 2 kg·m² = 2.5 rad/s².
Correct Answer: A — 2.5 rad/s²
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Q. If a torque of 8 Nm is produced by a force acting at a distance of 0.2 m, what is the force?
A.
20 N
B.
30 N
C.
40 N
D.
50 N
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Solution
Force = Torque / Distance = 8 Nm / 0.2 m = 40 N.
Correct Answer: A — 20 N
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Q. If a train travels at a speed of 72 km/h, how long will it take to cover a distance of 180 km?
A.
2 h
B.
2.5 h
C.
3 h
D.
3.5 h
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Solution
Time = distance / speed = 180 km / (72 km/h) = 2.5 h.
Correct Answer: C — 3 h
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Q. If a triangle has sides of lengths 3, 4, and 5, what is its area?
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Solution
The area of a right triangle is (1/2) * base * height = (1/2) * 3 * 4 = 6.
Correct Answer: A — 6
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Q. If a triangle has sides of lengths 3, 4, and 5, what type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
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Solution
A triangle with sides 3, 4, and 5 satisfies the Pythagorean theorem, thus it is a right triangle.
Correct Answer: C — Right
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Q. If a volume is measured as 200 L with an error of 5 L, what is the range of possible volumes?
A.
195 L to 205 L
B.
200 L to 205 L
C.
195 L to 210 L
D.
200 L to 210 L
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Solution
Range of possible volumes = 200 - 5 to 200 + 5 = 195 L to 205 L.
Correct Answer: A — 195 L to 205 L
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Q. If a weight is measured as 10 kg with a 0.2 kg error, what is the maximum possible true weight?
A.
10.2 kg
B.
9.8 kg
C.
10 kg
D.
10.4 kg
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Solution
Maximum true weight = Measured weight + Error = 10 kg + 0.2 kg = 10.2 kg.
Correct Answer: A — 10.2 kg
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Q. If a wheel of radius R rolls without slipping, what is the distance traveled by the center of mass after one complete rotation?
A.
2πR
B.
πR
C.
4R
D.
R/2
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Solution
The distance traveled by the center of mass after one complete rotation is equal to the circumference of the wheel, which is 2πR.
Correct Answer: A — 2πR
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Q. If a wire carries a current of 5 A and is placed in a magnetic field of 0.1 T, what is the force per unit length on the wire?
A.
0.5 N/m
B.
1 N/m
C.
0.2 N/m
D.
0.1 N/m
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Solution
Using the formula F = BIL, where B is the magnetic field, I is the current, and L is the length of the wire (1 m), F = 0.1 T * 5 A * 1 m = 0.5 N.
Correct Answer: B — 1 N/m
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Q. If a wire carries a current of 5 A, what is the magnetic field at a distance of 0.1 m from the wire?
A.
0.1 T
B.
0.2 T
C.
0.5 T
D.
1.0 T
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Solution
Using Ampere's Law, B = μ₀I/2πr, where μ₀ = 4π × 10^-7 Tm/A, we find B = (4π × 10^-7)(5)/(2π(0.1)) = 0.1 T.
Correct Answer: B — 0.2 T
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Q. If a wire carrying current I is bent into a semicircular arc of radius R, what is the magnetic field at the center of the arc?
A.
μ₀I/(4R)
B.
μ₀I/(2R)
C.
μ₀I/(8R)
D.
μ₀I/(πR)
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Solution
The magnetic field at the center of a semicircular arc of radius R carrying current I is given by B = μ₀I/(4R).
Correct Answer: A — μ₀I/(4R)
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Q. If a wire is bent into a semicircular shape, what is the magnetic field at the center of the semicircle due to current I?
A.
μ₀I/(4R)
B.
μ₀I/(2R)
C.
μ₀I/(πR)
D.
μ₀I/(8R)
Show solution
Solution
The magnetic field at the center of a semicircular wire carrying current I is given by B = μ₀I/(4R) for the semicircle, which is half of the full circular loop.
Correct Answer: C — μ₀I/(πR)
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Q. If a wire is bent into a semicircular shape, what is the magnetic field at the center of the semicircle due to the current I?
A.
μ₀I/(4R)
B.
μ₀I/(2R)
C.
μ₀I/(8R)
D.
μ₀I/(6R)
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Solution
The magnetic field at the center of a semicircular wire carrying current I is given by B = μ₀I/(4R).
Correct Answer: A — μ₀I/(4R)
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Q. If a wire is stretched and its length increases by 2%, what is the strain?
A.
0.02
B.
0.2
C.
2
D.
200
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Solution
Strain is defined as the change in length divided by the original length, so 2% = 0.02.
Correct Answer: A — 0.02
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Q. If a wire of length L and cross-sectional area A is stretched by a force F, what is the expression for the elongation?
A.
F * L / (A * E)
B.
A * F / (L * E)
C.
E * F / (A * L)
D.
L * E / (A * F)
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Solution
The elongation (ΔL) can be expressed as ΔL = F * L / (A * E).
Correct Answer: A — F * L / (A * E)
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Q. If a wire's length is doubled while keeping its cross-sectional area constant, how does its resistance change?
A.
Remains the same
B.
Doubles
C.
Halves
D.
Quadruples
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Solution
Resistance is directly proportional to length; doubling the length doubles the resistance.
Correct Answer: B — Doubles
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Q. If A(1, 2, 3) and B(4, 5, 6) are two points in space, what is the vector AB?
A.
(3, 3, 3)
B.
(2, 3, 4)
C.
(1, 1, 1)
D.
(0, 0, 0)
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Solution
Vector AB = B - A = (4-1, 5-2, 6-3) = (3, 3, 3).
Correct Answer: A — (3, 3, 3)
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Q. If A(1, 2, 3) and B(4, 5, 6) are two points, what is the vector AB?
A.
(3, 3, 3)
B.
(3, 3, 0)
C.
(0, 0, 0)
D.
(1, 1, 1)
Show solution
Solution
Vector AB = B - A = (4-1, 5-2, 6-3) = (3, 3, 3).
Correct Answer: A — (3, 3, 3)
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Q. If A(2, 3, 4) and B(1, 0, -1) are two points in space, find the vector AB.
A.
(1, 3, 5)
B.
(1, -3, -5)
C.
(1, 3, -5)
D.
(1, -3, 5)
Show solution
Solution
AB = B - A = (1 - 2, 0 - 3, -1 - 4) = (-1, -3, -5) = (1, 3, 5) in the opposite direction.
Correct Answer: A — (1, 3, 5)
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Q. If an electron has quantum numbers n=2, l=0, and m_l=0, which orbital does it occupy?
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Solution
The quantum numbers correspond to the 2s orbital, where l=0 indicates an s orbital.
Correct Answer: A — 2s
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Q. If an electron has quantum numbers n=3, l=1, and m_l=-1, what is the possible value of the spin quantum number?
A.
+1/2
B.
-1/2
C.
0
D.
1
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Solution
The spin quantum number can be either +1/2 or -1/2, so both values are possible.
Correct Answer: A — +1/2
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Q. If an electron has the quantum numbers n=3, l=1, m_l=0, what type of orbital does it occupy?
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Solution
For l=1, the electron occupies a p orbital.
Correct Answer: B — p
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Q. If an electron has the quantum numbers n=3, l=1, m_l=0, what type of orbital is it in?
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Solution
For l=1, the orbital is a p orbital.
Correct Answer: B — p
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Q. If an electron has the quantum numbers n=3, l=1, what is the possible range of m_l?
A.
-1, 0, +1
B.
0, +1, +2
C.
-2, -1, 0
D.
-1, 0, +1, +2
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Solution
For l=1, m_l can take values -1, 0, +1.
Correct Answer: A — -1, 0, +1
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Q. If an electron is in the state characterized by the quantum numbers n=4, l=0, what is the value of m_l?
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Solution
For l=0, m_l can only be 0.
Correct Answer: A — 0
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Q. If an electron is in the state characterized by the quantum numbers n=4, l=2, what is the value of m_l?
A.
-2
B.
0
C.
2
D.
All of the above
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Solution
For l=2, m_l can take values -2, -1, 0, 1, 2. Therefore, all of the options are valid.
Correct Answer: D — All of the above
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Q. If an ellipse has a semi-major axis of 10 and a semi-minor axis of 6, what is the value of b^2?
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Solution
For an ellipse, b is the semi-minor axis. Here, b = 6, so b^2 = 6^2 = 36.
Correct Answer: A — 36
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