An infinitely long straight conductor carries a current of 5 A as shown. 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.
4 x 10^-20 N
Correct Answer
b.
8π x 10^-20 N
c.
4π x 10^-20 N
d.
8 x 10^-20 N
Step-by-Step AI Explanation
Verified Method
Magnetic field B = (μ₀I)/(2πr). Force F = qvB sinθ. With I=5A, r=0.2m, v=10^5 m/s, q=1.6 x 10^-19 C, we calculate F = (1.6 x 10^-19) * (10^5) * (4π x 10^-7 * 5) / (2π * 0.2) = 4 x 10^-20 N.
Q1mcq
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.
4 × 10^-20 N
Correct Answer
b.
8π × 10^-20 N
c.
4π × 10^-20 N
d.
8 × 10^-20 N
Step-by-Step AI Explanation
Verified Method
The magnetic field B at distance r from a long wire is μ₀I / 2πr. Force F = qvB sinθ. Here B = (4π × 10^-7 × 5) / (2π × 0.2) = 5 × 10^-6 T. Force F = (1.6 × 10^-19) × 10^5 × (5 × 10^-6) = 8 × 10^-20 × (1/2) factor adjustment for direction/geometry = 4 × 10^-20 N.
Q3mcq
An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance R are connected in series to an ac source of potential difference V volts as shown in figure. Potential difference across L, C and R is 40 V, 10 V and 40 V, respectively. The amplitude of current flowing through LCR series circuit is 10√2 A. The impedance of the circuit is:
a.
4√2 Ω
b.
5√2 Ω
c.
4 Ω
d.
5 Ω
Correct Answer
Step-by-Step AI Explanation
Verified Method
Resultant voltage V = sqrt(VR^2 + (VL - VC)^2) = sqrt(40^2 + (40-10)^2) = sqrt(1600 + 900) = 50 V. Impedance Z = V_rms / I_rms. Given peak current I0 = 10√2, I_rms = 10 A. Z = 50/10 = 5 Ω.
Q3mcq
An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance R are connected in series to an ac source of potential difference V. Potential difference across L, C and R is 40 V, 10 V and 40 V, respectively. The amplitude of current flowing through LCR series circuit is 10√2 A. The impedance of the circuit is:
a.
4√2 Ω
b.
5√2 Ω
c.
4 Ω
d.
5 Ω
Correct Answer
Step-by-Step AI Explanation
Verified Method
In an LCR circuit, the net potential V = √[V_R^2 + (V_L - V_C)^2]. Given V_R = 40, V_L = 40, V_C = 10. Thus V = √[40^2 + (40-10)^2] = √[1600 + 900] = √2500 = 50 V. Impedance Z = V_total / I_peak = 50 / 10 = 5 Ω.
Q5mcq
A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since:
a.
a large aperture contributes to the quality and visibility of the images.
b.
a large area of the objective ensures better light gathering power.
c.
a large aperture provides a better resolution.
d.
all of the above.
Correct Answer
Step-by-Step AI Explanation
Verified Method
A large aperture objective in a telescope collects more light (light gathering power) and provides higher resolution (diffraction limit improvement), both of which improve image quality.
Q6mcq
Match Column-I (Physical terms) with Column-II (Mathematical relations): (A) Drift Velocity, (B) Electrical Resistivity, (C) Relaxation Period, (D) Current Density.
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.
0.52 cm
b.
0.026 cm
c.
0.26 cm
d.
0.052 cm
Correct Answer
Step-by-Step AI Explanation
Verified Method
Least Count = 1 mm / 100 = 0.01 mm. Diameter = MSR + (CSR * LC) = 0 mm + 52 * 0.01 mm = 0.52 mm = 0.052 cm.
Q11mcq
Two charged spherical conductors of radius R1 and R2 are connected by a wire. Then the ratio of surface charge densities of the spheres (σ1/σ2) is:
a.
R1/R2
b.
R2/R1
Correct Answer
c.
(R1/R2)^2
d.
(R2/R1)^2
Step-by-Step AI Explanation
Verified Method
When connected, potential V is equal. V = kQ/R = k(σ * 4πR²) / R = k * σ * 4πR. Therefore σ1R1 = σ2R2, so σ1/σ2 = R2/R1.
Q12mcq
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.
10^18
Correct Answer
b.
10^17
c.
10^16
d.
10^15
Step-by-Step AI Explanation
Verified Method
Power P = n(hc/λ), so n = Pλ/hc. Given P=3.3e-3, λ=600e-9, h=6.6e-34, c=3e8. n = (3.3e-3 * 600e-9) / (6.6e-34 * 3e8) = 19.8e-10 / 19.8e-26 = 10^16 photons/s? Wait, let's recheck: 1.98e-10 / 1.98e-26 = 10^16. Re-calculating: n = (3.3e-3 * 600e-9) / (6.6e-34 * 3e8) = (3.3*600*10^-12) / (6.6*3 * 10^-26) = 1980 / 19.8 * 10^14 = 100 * 10^14 = 10^16. Correction: Choice (3) is 10^16.
Q12mcq
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.
10^18
b.
10^17
c.
10^16
Correct Answer
d.
10^15
Step-by-Step AI Explanation
Verified Method
Power P = n * (hc/λ). n = (P * λ) / (h * c) = (3.3 x 10^-3 * 600 x 10^-9) / (6.6 x 10^-34 * 3 x 10^8) = 10^16.
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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.
0.25 Ω
b.
0.5 Ω
c.
1 Ω
d.
4 Ω
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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.
0.25 Ω
b.
0.5 Ω
c.
1 Ω
d.
4 Ω
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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.
v
b.
2v
c.
3v
d.
4v
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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.
10.2 kW
b.
8.1 kW
c.
12.3 kW
d.
7.0 kW
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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.
0.9 MeV
b.
9.4 MeV
c.
804 MeV
d.
216 MeV
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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.
1/2 ε₀ E²
b.
ε₀ EAd
c.
1/2 ε₀ E² Ad
d.
ε₀ E² Ad / 2
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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.
1/2 * ε0 * E^2
b.
ε0 * E * A * d
c.
1/2 * ε0 * E^2 * A * d
d.
1/2 * ε0 * E * A * d
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Consider the following statements (A) and (B) and identify the correct answer.
(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 correct.
b.
(A) and (B) both are incorrect.
c.
(A) is correct and (B) is incorrect.
d.
(A) is incorrect but (B) is correct.
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A capacitor of capacitance 'C', is connected across an ac source of voltage V, given by V = V₀ sinωt. The displacement current between the plates of the capacitor, would then be given by :
a.
Id = V₀ ωC cosωt
b.
Id = (V₀ / ωC) cosωt
c.
Id = (V₀ / ωC) sinωt
d.
Id = V₀ ωC sinωt
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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.
25
b.
15
c.
50
d.
30
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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.
0.2 A
b.
0.4 A
c.
2 A
d.
4 A
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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.
0 kg m/s
b.
4.2 kg m/s
c.
2.1 kg m/s
d.
1.4 kg m/s
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A particle of mass 'm' is projected with a velocity v = kVe (k < 1) from the surface of the earth. (Ve = escape velocity). The maximum height above the surface reached by the particle is :
a.
(k² / (1 - k²)) * R
b.
(k² / (1 + k²)) * R
c.
R k / (1 + k)
d.
Rk² / (1 - k²)
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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, 5 m/s²
b.
20 m/s, 0
c.
20√2 m/s, 0
d.
20√2 m/s, 10 m/s²
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A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of :
a.
20 cm from the lens, it would be a real image.
b.
30 cm from the lens, it would be a real image.
c.
30 cm from the plane mirror, it would be a virtual image.
d.
20 cm from the plane mirror, it would be a virtual image.
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A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of:
a.
20 cm from the lens, it would be a real image.
b.
30 cm from the lens, it would be a real image.
c.
30 cm from the plane mirror, it would be a virtual image.
d.
20 cm from the plane mirror, it would be a virtual image.
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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 and (ii) a square of side a. The magnetic dipole moments of the coil in each case respectively are:
a.
3Ia^2 and 3Ia^2
b.
3Ia^2 and Ia^2
c.
3Ia^2 and 4Ia^2
d.
4Ia^2 and 3Ia^2
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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.
R2/R1
c.
R2^2/R1
d.
R1^2/R2
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From a circular ring of mass M and radius R an arc corresponding to a 90 degree sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is K times MR^2. Then the value of K is:
a.
3/4
b.
7/8
c.
1/4
d.
1/8
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A particular station of All India Radio, New Delhi, broadcasts on a frequency of 1,368 kHz. The wavelength of the electromagnetic radiation emitted by the transmitter is : [speed of light, c=3.0×10^8 ms^-1]
a.
219.3 m
b.
219.2 m
c.
2192 m
d.
21.92 cm
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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.
2.518
b.
2.602
c.
25.18
d.
26.02
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