A parallel plate capacitor has a uniform electric field ‘E’ in the space between the plates. If the distance between the plates is ‘d’ and the area of each plate is ‘A’, the energy stored in the capacitor is: (ε₀ = permittivity of free space)
a.
ε₀EAd
b.
(1/2)ε₀E²Ad
Correct Answer
c.
E²Ad/ε₀
d.
(1/2)ε₀E²
Step-by-Step AI Explanation
Verified Method
Energy density (u) in a capacitor is (1/2)ε₀E². Total energy stored is u × Volume. Volume = Ad. Thus, Energy = (1/2)ε₀E²Ad.
Q1mcq
A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and the area of each plate is A, the energy stored in the capacitor is: (ε0 = permittivity of free space)
a.
ε0EAd
b.
1/2 ε0E^2 Ad
Correct Answer
c.
ε0E^2 Ad
d.
1/2 ε0E^2
Step-by-Step AI Explanation
Verified Method
Energy density (u) in a capacitor is given by u = 1/2 ε0E^2. Total energy U = u * Volume = (1/2 ε0E^2) * (A * d).
Q2mcq
The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d/2, then the viscous force acting on the ball will be:
a.
Mg
b.
3Mg/2
c.
2Mg
d.
Mg/2
Correct Answer
Step-by-Step AI Explanation
Verified Method
When terminal velocity is reached, forces are balanced: Weight = Buoyant force + Viscous force. Mg = (Volume * (d/2) * g) + Fv. Since M = Volume * d, Buoyant force = Mg/2. Thus, Fv = Mg - Mg/2 = Mg/2.
Q2mcq
The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d/2, then the viscous force acting on the ball will be:
a.
Mg
b.
3/2 Mg
c.
2 Mg
d.
Mg/2
Correct Answer
Step-by-Step AI Explanation
Verified Method
When velocity is constant (terminal velocity), the net force is zero. Weight = Buoyant force + Viscous force. Mg = (Density of liquid * Volume * g) + Viscous force. Since d_liquid = d/2 and d_solid = d, Volume = M/d. Buoyant force = (d/2) * (M/d) * g = Mg/2. Viscous force = Mg - Mg/2 = Mg/2.
Q3mcq
The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section and same material is 0.25 Ω. What will be the effective resistance if they are connected in series?
a.
0.5 Ω
b.
1 Ω
c.
4 Ω
Correct Answer
d.
0.25 Ω
Step-by-Step AI Explanation
Verified Method
Let resistance of each wire be R. In parallel, R/4 = 0.25, so R = 1 Ω. In series, R_eff = R + R + R + R = 4R = 4(1) = 4 Ω.
Q3mcq
The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section and same material is 0.25 Ω. What will be the effective resistance if they are connected in series?
a.
0.5 Ω
b.
1 Ω
c.
4 Ω
Correct Answer
d.
0.25 Ω
Step-by-Step AI Explanation
Verified Method
In parallel, R_eq = R/n. 0.25 = R/4 => R = 1 Ω. In series, R_eq = nR = 4 * 1 = 4 Ω.
Q4mcq
A convex lens A of focal length 20 cm and a concave lens B of focal length 5 cm are kept along the same axis with a distance d between them. If a parallel beam of light falling on A leaves B as a parallel beam, then the distance d in cm will be:
a.
15
Correct Answer
b.
50
c.
30
d.
25
Step-by-Step AI Explanation
Verified Method
For a parallel beam to emerge, the image formed by the convex lens (at its focus f1=20cm) must act as a virtual object at the focus of the concave lens (f2=5cm). Therefore, distance d = |f1| - |f2| = 20 - 5 = 15 cm.
Q4mcq
A convex lens ‘A’ of focal length 20 cm and a concave lens ‘B’ of focal length 5 cm are kept along the same axis with a distance ‘d’ between them. If a parallel beam of light falling on ‘A’ leaves ‘B’ as a parallel beam, then the distance ‘d’ in cm will be:
a.
15
Correct Answer
b.
50
c.
30
d.
25
Step-by-Step AI Explanation
Verified Method
For the light to emerge parallel from the concave lens, the rays must be directed towards the focal point of the concave lens. Thus, d = f_convex - |f_concave| = 20 - 5 = 15 cm.
Q5mcq
If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.
a.
[F] [A] [T²]
Correct Answer
b.
[F] [A] [T⁻¹]
c.
[F] [A⁻¹] [T]
d.
[F] [A] [T]
Step-by-Step AI Explanation
Verified Method
Energy = Work = Force * Displacement. Displacement = (1/2) * Acceleration * Time². Therefore, Energy = [F] [A] [T²].
Q6mcq
Match Column I with Column II based on current flow through a metallic conductor.
a.
(A)-(R), (B)-(S), (C)-(Q), (D)-(P)
b.
(A)-(R), (B)-(P), (C)-(S), (D)-(Q)
c.
(A)-(R), (B)-(Q), (C)-(S), (D)-(P)
d.
(A)-(R), (B)-(S), (C)-(P), (D)-(Q)
Correct Answer
Step-by-Step AI Explanation
Verified Method
Drift Velocity vd = (eE/m)τ (R). Resistivity ρ = E/J (S). Relaxation time τ = 2m/ne²ρ (P). Current Density J = nev_d (Q).
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A cup of coffee cools from 90°C to 80°C in t minutes, when the room temperature is 20°C. The time taken by a similar cup of coffee to cool from 80°C to 60°C at a room temperature same at 20°C is:
a.
13t/5
b.
10t/13
c.
5t/13
d.
13t/10
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An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance R are connected in series. Potential difference across L, C and R is 40 V, 10 V and 40 V, respectively. The amplitude of current is 10√2 A. The impedance of the circuit is:
a.
5√2 Ω
b.
4 Ω
c.
5 Ω
d.
4√2 Ω
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Consider the following statements (A) and (B): (A) A zener diode is connected in reverse bias, when used as a voltage regulator. (B) The potential barrier of p-n junction lies between 0.1 V to 0.3 V.
a.
(A) and (B) both are incorrect.
b.
(A) is correct and (B) is incorrect.
c.
(A) is incorrect but (B) is correct.
d.
(A) and (B) both are correct.
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In a potentiometer circuit a cell of EMF 1.5 V gives balance point at 36 cm length of wire. If another cell of EMF 2.5 V replaces the first cell, then at what length of the wire, the balance point occurs?
a.
21.6 cm
b.
64 cm
c.
62 cm
d.
60 cm
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In a potentiometer circuit a cell of EMF 1.5 V gives balance point at 36 cm length of wire. If another cell of EMF 2.5 V replaces the first cell, then at what length of the wire, the balance point occurs?
a.
21.6 cm
b.
64 cm
c.
62 cm
d.
60 cm
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The escape velocity from the Earth’s surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is:
a.
2 v
b.
3 v
c.
4 v
d.
v
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The escape velocity from the Earth’s surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is:
a.
2v
b.
3v
c.
4v
d.
v
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A screw gauge gives the following readings when used to measure the diameter of a wire. Main scale reading: 0 mm. Circular scale reading: 52 divisions. Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is:
a.
0.026 cm
b.
0.26 cm
c.
0.052 cm
d.
0.52 cm
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A capacitor of capacitance ‘C’, is connected across an ac source of voltage V, given by V=V0 sin(ωt). The displacement current between the plates of the capacitor, would then be given by:
a.
Id = V0 ωC cos(ωt)
b.
Id = V0 / (ωC) sin(ωt)
c.
Id = V0 ωC sin(ωt)
d.
Id = V0 ωC cos(ωt)
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The number of photons per second on an average emitted by the source of monochromatic light of wavelength 600 nm, when it delivers the power of 3.3×10^-3 watt will be : (h=6.6×10^-34 Js)
a.
10^17
b.
10^16
c.
10^15
d.
10^18
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The electron concentration in an n-type semiconductor is the same as hole concentration in a p-type semiconductor. An external field (electric) is applied across each of them. Compare the currents in them.
a.
current in p-type > current in n-type.
b.
current in n-type > current in p-type.
c.
No current will flow in p-type, current will only flow in n-type.
d.
current in n-type=current in p-type.
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A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the Binding Energy in the process is:
a.
9.4 MeV
b.
804 MeV
c.
216 MeV
d.
0.9 MeV
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A small block slides down on a smooth inclined plane, starting from rest at time t=0. Let Sn be the distance travelled by the block in the interval t=n-1 to t=n. Then, the ratio Sn / Sn+1 is:
a.
(2n-1)/(2n+1)
b.
(2n+1)/(2n-1)
c.
2n/(2n-1)
d.
(2n-1)/2n
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A small block slides down on a smooth inclined plane, starting from rest at time t=0. Let Sn be the distance travelled by the block in the interval t=n-1 to t=n. Then, the ratio Sn / Sn+1 is:
a.
(2n-1)/(2n+1)
b.
(2n+1)/(2n-1)
c.
2n/(2n-1)
d.
(2n-1)/2n
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A particle is released from height S from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are respectively:
a.
3S/4, sqrt(3gS/2)
b.
3S/2, sqrt(3gS/2)
c.
S/4, sqrt(3gS/2)
d.
S/4, sqrt(3gS/4)
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A radioactive nucleus (A, Z)X undergoes spontaneous decay in the sequence (A, Z)X -> (A, Z-1)B -> (A, Z-3)C -> (A, Z-2)D, where Z is the atomic number of element X. The possible decay particles in the sequence are:
a.
α, β+, β-
b.
β+, α, β-
c.
β-, α, β+
d.
α, β-, β+
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An infinitely long straight conductor carries a current of 5 A. An electron is moving with a speed of 10^5 m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm at an instant. Calculate the magnitude of the force experienced by the electron at that instant.
a.
8π×10^-20 N
b.
4π×10^-20 N
c.
8×10^-20 N
d.
4×10^-20 N
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Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? (g=10 m/s^2)
a.
8.1 kW
b.
12.3 kW
c.
7.0 kW
d.
10.2 kW
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A series LCR circuit containing 5.0 H inductor, 80 µF capacitor and 40 Ω resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be:
a.
50 rad/s and 25 rad/s
b.
46 rad/s and 54 rad/s
c.
42 rad/s and 58 rad/s
d.
25 rad/s and 75 rad/s
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Three resistors having resistances r1, r2 and r3 are connected as shown in the given circuit. The ratio i3/i1 of currents in terms of resistances used in the circuit is:
a.
r2 / (r2 + r3)
b.
r1 / (r1 + r2)
c.
r2 / (r1 + r3)
d.
r1 / (r2 + r3)
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Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 >> R2, the mutual inductance M between them will be directly proportional to :
a.
R2 / R1
b.
R2^2 / R1
c.
R2^2 / R1^2
d.
R1 / R2
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Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 >> R2, the mutual inductance M between them will be directly proportional to:
a.
R1/R2
b.
R1^2/R2
c.
R2^2/R1
d.
R1/R2^2
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A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is (g=10 m/s2) nearly :
a.
4.2 kg m/s
b.
2.1 kg m/s
c.
1.4 kg m/s
d.
0 kg m/s
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A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is (g=10 m/s^2) nearly:
a.
4.2 kg m/s
b.
2.1 kg m/s
c.
1.4 kg m/s
d.
0 kg m/s
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A car starts from rest and accelerates at 5 m/s2. At t=4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t=6 s ? (Take g=10 m/s2)
a.
20 m/s, 0
b.
20 sqrt(2) m/s, 0
c.
20 sqrt(2) m/s, 10 m/s2
d.
20 m/s, 5 m/s2
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A uniform conducting wire of length 12a and resistance ‘R’ is wound up as a current carrying coil in the shape of, (i) an equilateral triangle of side ‘a’. (ii) a square of side ‘a’. The magnetic dipole moments of the coil in each case respectively are :
a.
3 Ia^2 and Ia^2
b.
3 Ia^2 and 4 Ia^2
c.
4 Ia^2 and 3 Ia^2
d.
3 Ia^2 and 3 Ia^2
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A step down transformer connected to an ac mains supply of 220 V is made to operate at 11 V, 44 W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit ?
a.
0.4 A
b.
2 A
c.
4 A
d.
0.2 A
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A particular station of All India Radio, New Delhi, broadcasts on a frequency of 1,368 kHz (kilohertz). The wavelength of the electromagnetic radiation emitted by the transmitter is : [speed of light, c=3.0×10^8 ms^-1]
a.
219.2 m
b.
2192 m
c.
21.92 cm
d.
219.3 m
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Choose the correct option for the total pressure (in atm.) in a mixture of 4 g O2 and 2 g H2 confined in a total volume of one litre at 0°C is: [Given R=0.082 L atm mol^-1 K^-1, T=273 K]
a.
2.602
b.
25.18
c.
26.02
d.
2.518
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