Q. If a 5 kg object is in free fall, what is the force acting on it due to gravity?
A.
5 N
B.
10 N
C.
50 N
D.
15 N
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Solution
The force due to gravity F = mg = 5 kg * 10 m/s² = 50 N.
Correct Answer: C — 50 N
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Q. If a 5 kg object is lifted to a height of 10 m, what is the potential energy gained by the object? (g = 9.8 m/s²)
A.
490 J
B.
980 J
C.
245 J
D.
2450 J
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Solution
Potential Energy = mass × g × height = 5 kg × 9.8 m/s² × 10 m = 490 J.
Correct Answer: B — 980 J
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Q. If a 5 kg object is lifted to a height of 10 m, what is the work done against gravity? (g = 9.8 m/s²)
A.
49 J
B.
98 J
C.
490 J
D.
980 J
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Solution
Work done = mgh = 5 kg × 9.8 m/s² × 10 m = 490 J.
Correct Answer: C — 490 J
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Q. If a 5 kg object is lifted to a height of 10 m, what is the work done against gravity?
A.
50 J
B.
100 J
C.
150 J
D.
200 J
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Solution
Work done = mgh = 5 kg × 9.8 m/s² × 10 m = 490 J.
Correct Answer: D — 200 J
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Q. If a 5 kg object is subjected to a force of 20 N, what is its acceleration?
A.
2 m/s²
B.
4 m/s²
C.
5 m/s²
D.
10 m/s²
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Solution
Using F = ma, acceleration a = F/m = 20 N / 5 kg = 4 m/s².
Correct Answer: B — 4 m/s²
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Q. If a 5 ohm resistor and a 10 ohm resistor are connected in series, what is the voltage across the 10 ohm resistor when a current of 2 A flows through the circuit?
A.
10 V
B.
20 V
C.
5 V
D.
15 V
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Solution
Voltage across the 10 ohm resistor, V = I * R = 2 A * 10 Ω = 20 V.
Correct Answer: B — 20 V
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Q. If a 5 ohm resistor is connected to a 10V battery, what is the energy consumed in 2 seconds?
A.
10 J
B.
20 J
C.
5 J
D.
15 J
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Solution
Power P = V^2 / R = 10^2 / 5 = 20 W. Energy = Power * time = 20 W * 2 s = 40 J.
Correct Answer: B — 20 J
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Q. If a 5 ohm resistor is connected to a 10V battery, what is the energy consumed in 2 minutes?
A.
60 J
B.
120 J
C.
240 J
D.
30 J
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Solution
Power P = V^2/R = 10^2 / 5 = 20 W. Energy = Power * time = 20 W * 120 s = 2400 J.
Correct Answer: B — 120 J
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Q. If a 5Ω resistor is connected in parallel with a 10Ω resistor, what is the equivalent resistance?
A.
3.33Ω
B.
5Ω
C.
7.5Ω
D.
15Ω
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Solution
R_eq = 1/(1/5 + 1/10) = 3.33Ω.
Correct Answer: A — 3.33Ω
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Q. If a 6 kg object is subjected to a net force of 24 N, what is its acceleration?
A.
4 m/s²
B.
6 m/s²
C.
8 m/s²
D.
10 m/s²
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Solution
Using F = ma, acceleration a = F/m = 24 N / 6 kg = 4 m/s².
Correct Answer: A — 4 m/s²
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Q. If a 60W bulb operates at 120V, what is the resistance of the bulb?
A.
240 ohms
B.
120 ohms
C.
60 ohms
D.
30 ohms
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Solution
Using P = V^2 / R, R = V^2 / P = (120V)^2 / 60W = 240 ohms.
Correct Answer: B — 120 ohms
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Q. If a 60W light bulb operates at 120V, what is the resistance of the bulb?
A.
240 ohms
B.
120 ohms
C.
60 ohms
D.
30 ohms
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Solution
Power (P) = V^2 / R, so R = V^2 / P = (120V)^2 / 60W = 240 ohms.
Correct Answer: B — 120 ohms
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Q. If a 6V battery is connected to a circuit with a total resistance of 3 ohms, what is the current flowing through the circuit?
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Solution
Using Ohm's law, I = V/R = 6V / 3 ohms = 2A.
Correct Answer: B — 2A
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Q. If a 6Ω resistor is connected to a 9V battery, what is the power dissipated by the resistor?
A.
6W
B.
9W
C.
12W
D.
15W
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Solution
Power P = V^2 / R = (9V)^2 / 6Ω = 81 / 6 = 13.5W.
Correct Answer: C — 12W
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Q. If a 9V battery is connected to a 3Ω resistor, what is the power consumed by the resistor?
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Solution
Power P = V^2/R = (9V)^2 / 3Ω = 81/3 = 27W.
Correct Answer: B — 9W
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Q. If A = (1, 0) and B = (0, 1), what is the angle between them?
A.
0 degrees
B.
90 degrees
C.
45 degrees
D.
180 degrees
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Solution
Angle = cos⁻¹((A·B) / (|A||B|)) = cos⁻¹(0) = 90 degrees
Correct Answer: B — 90 degrees
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Q. If A = (1, 0, -1) and B = (0, 1, 1), what is the scalar product A · B?
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Solution
A · B = 1*0 + 0*1 + (-1)*1 = 0 + 0 - 1 = -1.
Correct Answer: A — 0
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Q. If A = (1, 0, 0) and B = (0, 1, 0), what is the value of A · B?
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Solution
A · B = 1*0 + 0*1 + 0*0 = 0.
Correct Answer: A — 0
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Q. If A = (1, 0, 0) and B = (0, 1, 0), what is the vector product A × B?
A.
(0, 0, 1)
B.
(1, 0, 0)
C.
(0, 1, 0)
D.
(0, 0, 0)
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Solution
A × B = (0, 0, 1) using the right-hand rule.
Correct Answer: A — (0, 0, 1)
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Q. If A = (1, 1, 1) and B = (1, 1, 1), what is the scalar product A · B?
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Solution
A · B = 1*1 + 1*1 + 1*1 = 3.
Correct Answer: C — 3
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Q. If A = (1, 1, 1) and B = (2, 2, 2), what is A × B?
A.
(0, 0, 0)
B.
(1, 1, 1)
C.
(2, 2, 2)
D.
(3, 3, 3)
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Solution
A × B = (0, 0, 0) since A and B are parallel.
Correct Answer: A — (0, 0, 0)
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Q. If A = (1, 1, 1) and B = (2, 2, 2), what is the scalar product A · B?
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Solution
A · B = 1*2 + 1*2 + 1*2 = 2 + 2 + 2 = 6.
Correct Answer: B — 6
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Q. If A = (1, 1, 1) and B = (x, y, z) such that A · B = 3, what is the value of x + y + z?
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Solution
A · B = 1*x + 1*y + 1*z = x + y + z = 3.
Correct Answer: C — 3
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Q. If A = (1, 2) and B = (3, 4), what is the dot product A · B?
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Solution
Dot product A · B = 1*3 + 2*4 = 3 + 8 = 11.
Correct Answer: A — 10
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Q. If A = (1, 2) and B = (3, 4), what is the midpoint M of AB?
A.
(2, 3)
B.
(1, 2)
C.
(3, 4)
D.
(4, 5)
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Solution
Midpoint M = ((1+3)/2, (2+4)/2) = (2, 3).
Correct Answer: A — (2, 3)
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Q. If A = (1, 2, 3) and B = (0, 1, 0), what is the direction of the vector product A × B?
A.
(2, -3, 1)
B.
(3, 0, -1)
C.
(1, 0, -1)
D.
(1, 3, 0)
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Solution
A × B = (2, -3, 1) gives direction (2, -3, 1).
Correct Answer: B — (3, 0, -1)
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Q. If A = (1, 2, 3) and B = (4, 5, 6), what is the magnitude of the vector product A × B?
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Solution
Magnitude |A × B| = √(1^2 + 2^2 + 3^2) = √14.
Correct Answer: D — √14
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Q. If A = (1, 2, 3) and B = (4, 5, 6), what is the value of A · B?
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Solution
A · B = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.
Correct Answer: B — 30
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Q. If A = (1, 2, 3) and B = (k, k, k) are perpendicular, what is the value of k?
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Solution
A · B = 1*k + 2*k + 3*k = 6k = 0. Thus, k = 0.
Correct Answer: D — 0
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Q. If A = (1, 2, 3) and B = (x, y, z) are such that A · B = 0, what is the condition for x, y, z?
A.
x + 2y + 3z = 0
B.
x - 2y + 3z = 0
C.
x + 2y - 3z = 0
D.
x - 2y - 3z = 0
Show solution
Solution
A · B = 1*x + 2*y + 3*z = 0 gives the condition x + 2y + 3z = 0.
Correct Answer: A — x + 2y + 3z = 0
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