Q. A capacitor is charged to a potential difference of 12 V. If the capacitance is 4 µF, what is the charge stored in the capacitor?
A.12 µC
B.24 µC
C.48 µC
D.36 µC
Solution
Charge Q is given by Q = CV. Here, Q = 4 µF * 12 V = 48 µC.
Correct Answer: B — 24 µC
Q. A capacitor is charged to a potential difference of V. What is the energy stored in the capacitor?
A.1/2 CV²
B.CV
C.V²/C
D.1/2 QV
Solution
The energy (U) stored in a capacitor is given by U = 1/2 CV², where C is the capacitance and V is the potential difference.
Correct Answer: A — 1/2 CV²
Q. A capacitor is charged to a potential of 12 V. If the capacitance is 3 µF, what is the energy stored in the capacitor?
A.0.18 mJ
B.0.36 mJ
C.0.54 mJ
D.0.72 mJ
Solution
Energy stored in a capacitor is given by U = 1/2 CV² = 1/2 * 3 x 10^-6 F * (12 V)² = 0.36 mJ.
Correct Answer: B — 0.36 mJ
Q. A capacitor is charged to a potential of V. If the charge on the capacitor is doubled, what will be the new potential?
A.V
B.2V
C.V/2
D.4V
Solution
The potential V across a capacitor is directly proportional to the charge. If the charge is doubled, the potential also doubles.
Correct Answer: B — 2V
Q. A capacitor is charged to a voltage V and then disconnected from the battery. If the distance between the plates is doubled, what happens to the voltage across the capacitor?
A.It doubles
B.It halves
C.It remains the same
D.It quadruples
Solution
When the distance is doubled, the capacitance decreases, leading to an increase in voltage since Q = CV is constant.
Correct Answer: A — It doubles
Q. A capacitor is charged to a voltage V and then disconnected from the battery. If the distance between the plates is increased, what happens to the charge?
A.Increases
B.Decreases
C.Remains the same
D.Becomes zero
Solution
When a capacitor is disconnected from the battery, the charge remains constant. Increasing the distance decreases capacitance but does not affect the charge.
Correct Answer: C — Remains the same
Q. A capacitor is charged to a voltage V and then disconnected from the battery. What happens to the charge on the capacitor if the voltage is doubled?
A.Charge doubles
B.Charge halves
C.Charge remains the same
D.Charge quadruples
Solution
The charge on a capacitor is given by Q = C * V. If the voltage is doubled, the charge also doubles, assuming capacitance remains constant.
Correct Answer: A — Charge doubles
Q. A capacitor is charged to a voltage V and then disconnected from the battery. What happens to the charge on the capacitor if the distance between the plates is increased?
A.Charge increases
B.Charge decreases
C.Charge remains the same
D.Charge becomes zero
Solution
When a capacitor is disconnected from the battery, the charge remains constant. Increasing the distance decreases capacitance but does not change the charge.
Correct Answer: C — Charge remains the same
Q. A capacitor is charged to a voltage V and then the voltage is halved. What happens to the energy stored in the capacitor?
A.It doubles
B.It halves
C.It remains the same
D.It becomes zero
Solution
The energy stored in a capacitor is proportional to the square of the voltage (U = 1/2 CV²). If the voltage is halved, the energy becomes U/4.
Correct Answer: B — It halves
Q. A capacitor of capacitance 10μF is charged to a potential difference of 100V. What is the energy stored in the capacitor?
A.0.05 J
B.0.1 J
C.0.2 J
D.0.3 J
Solution
Energy stored, U = 1/2 * C * V^2 = 1/2 * 10 × 10^-6 * (100)^2 = 0.05 J.
Correct Answer: B — 0.1 J
Q. A capacitor of capacitance 10μF is charged to a potential of 100V. What is the energy stored in the capacitor?
A.0.05 J
B.0.1 J
C.0.2 J
D.0.01 J
Solution
Energy stored in a capacitor is given by U = 1/2 CV² = 1/2 * 10 × 10^-6 F * (100 V)² = 0.05 J.
Correct Answer: B — 0.1 J
Q. A capacitor of capacitance 5μF is charged to a potential of 10V. What is the energy stored in the capacitor?
A.0.25 mJ
B.0.5 mJ
C.1 mJ
D.2.5 mJ
Solution
Energy stored U = 1/2 * C * V² = 1/2 * 5 × 10^-6 F * (10 V)² = 0.5 mJ.
Correct Answer: B — 0.5 mJ
Q. A capacitor of capacitance C is charged to a voltage V and then connected in parallel with another uncharged capacitor of capacitance C. What is the final voltage across the capacitors?
A.V/2
B.V
C.2V
D.0
Solution
When connected in parallel, the total charge is conserved. The final voltage across both capacitors is V/2.
Correct Answer: A — V/2
Q. A capacitor of capacitance C is connected to a battery of voltage V. If the battery is removed and the capacitor is connected to another capacitor of capacitance 2C, what is the final voltage across the combination?
A.V/3
B.V/2
C.V
D.2V
Solution
When the charged capacitor C is connected to an uncharged capacitor 2C, the final voltage is V_final = Q_total / C_eq = V/(1 + 1/2) = V/3.
Correct Answer: B — V/2
Q. A capillary tube is dipped in water. What is the shape of the water surface inside the tube?
A.Flat
B.Concave
C.Convex
D.Irregular
Solution
The water surface inside the capillary tube is concave due to the adhesive forces between water and the tube material being stronger than the cohesive forces among water molecules.
Correct Answer: B — Concave
Q. A capillary tube is dipped into water. How high will the water rise in the tube if the radius is 1 mm?
A.2.5 cm
B.5 cm
C.10 cm
D.15 cm
Solution
Using the capillary rise formula, h = (2γcosθ)/(ρgr), where γ is surface tension, θ is contact angle, ρ is density, g is acceleration due to gravity, and r is radius.
Correct Answer: B — 5 cm
Q. A capillary tube is dipped into water. The height to which water rises in the tube is determined by:
A.Surface tension and density of the liquid
B.Only surface tension
C.Only density of the liquid
D.Viscosity of the liquid
Solution
The height of the liquid column in a capillary tube is determined by both surface tension and the density of the liquid, as described by the capillary rise formula.
Correct Answer: A — Surface tension and density of the liquid
Q. A capillary tube is dipped into water. What will happen to the water level inside the tube?
A.It will rise
B.It will fall
C.It will remain the same
D.It will oscillate
Solution
The water will rise in the capillary tube due to capillary action, which is a result of surface tension.
Correct Answer: A — It will rise
Q. A car accelerates from rest at a rate of 2 m/s². What is the net force acting on the car if its mass is 1000 kg?
A.200 N
B.500 N
C.1000 N
D.2000 N
Solution
Using F = ma, F = 1000 kg * 2 m/s² = 2000 N.
Correct Answer: D — 2000 N
Q. A car accelerates from rest to a speed of 20 m/s in 10 seconds. What is the distance covered by the car during this time?
A.50 m
B.100 m
C.200 m
D.400 m
Solution
Using the formula d = ut + 0.5at², where u = 0, a = (20 m/s) / 10 s = 2 m/s², we get d = 0 + 0.5 * 2 * (10)² = 100 m.
Correct Answer: B — 100 m
Q. A car accelerates from rest to a speed of 30 m/s. If the mass of the car is 800 kg, what is the work done on the car?
A.360,000 J
B.480,000 J
C.600,000 J
D.720,000 J
Solution
Work done = Change in Kinetic Energy = 0.5 × mass × (final speed² - initial speed²) = 0.5 × 800 kg × (30 m/s)² = 360,000 J.
Correct Answer: B — 480,000 J
Q. A car accelerates uniformly from rest to a speed of 20 m/s in 10 seconds. What is the distance covered by the car during this time?
A.100 m
B.200 m
C.300 m
D.400 m
Solution
Using the formula: distance = initial velocity * time + 0.5 * acceleration * time^2. Here, initial velocity = 0, final velocity = 20 m/s, time = 10 s. Acceleration = (final velocity - initial velocity) / time = 2 m/s². Distance = 0 + 0.5 * 2 * 10² = 100 m.
Correct Answer: B — 200 m
Q. A car engine does 3000 J of work in 5 seconds. What is the average power output of the engine?
A.600 W
B.800 W
C.1000 W
D.1200 W
Solution
Using the formula P = W/t, we find P = 3000 J / 5 s = 600 W.
Correct Answer: C — 1000 W
Q. A car engine does 3000 J of work in 5 seconds. What is the power of the engine?
A.600 W
B.800 W
C.1000 W
D.1200 W
Solution
Using the formula P = W/t, we have P = 3000 J / 5 s = 600 W.
Correct Answer: A — 600 W
Q. A car is moving at 80 km/h and a motorcycle at 60 km/h in the same direction. What is the relative speed of the motorcycle with respect to the car?
A.20 km/h
B.60 km/h
C.80 km/h
D.140 km/h
Solution
Relative speed = Speed of motorcycle - Speed of car = 60 km/h - 80 km/h = -20 km/h (20 km/h behind).
Correct Answer: A — 20 km/h
Q. A car is moving at 80 km/h and a motorcycle is moving at 100 km/h in the same direction. What is the speed of the motorcycle relative to the car?
A.20 km/h
B.80 km/h
C.100 km/h
D.180 km/h
Solution
Relative speed = Speed of motorcycle - Speed of car = 100 km/h - 80 km/h = 20 km/h.
Correct Answer: A — 20 km/h
Q. A car is moving at 80 km/h and a motorcycle is moving at 100 km/h in the same direction. What is the relative speed of the motorcycle with respect to the car?
A.20 km/h
B.180 km/h
C.100 km/h
D.80 km/h
Solution
Relative speed = Speed of motorcycle - Speed of car = 100 km/h - 80 km/h = 20 km/h.
Correct Answer: A — 20 km/h
Q. A car is moving at 80 km/h and a motorcycle is moving at 60 km/h in the same direction. What is the speed of the motorcycle relative to the car?
A.20 km/h
B.60 km/h
C.80 km/h
D.140 km/h
Solution
Relative speed = Speed of motorcycle - Speed of car = 60 km/h - 80 km/h = -20 km/h (20 km/h behind the car).
Correct Answer: A — 20 km/h
Q. A car is moving at 80 km/h and a motorcycle is moving at 60 km/h in the same direction. What is the relative speed of the motorcycle with respect to the car?
A.20 km/h
B.60 km/h
C.80 km/h
D.140 km/h
Solution
Relative speed = Speed of motorcycle - Speed of car = 60 km/h - 80 km/h = -20 km/h (20 km/h behind).
Correct Answer: A — 20 km/h
Q. A car is moving in a circular path of radius 50 m with a constant speed of 20 m/s. What is the centripetal acceleration of the car?
