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.
4 v
Correct Answer
b.
v
c.
2 v
d.
3 v
Step-by-Step AI Explanation
Verified Method
Escape velocity v = sqrt(2GM/R). Since density rho = M / ((4/3)piR^3), M = (4/3)piR^3 * rho. Substituting M, v is proportional to sqrt(R^3 * rho / R) = R * sqrt(rho). If radius becomes 4 times and density is same, v becomes 4 times.
Q1mcq
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.
4v
Correct Answer
b.
v
c.
2v
d.
3v
Step-by-Step AI Explanation
Verified Method
Escape velocity v_e = sqrt(2GM/R). Since M = density * volume = (4/3)πR³ρ, v_e is proportional to R*sqrt(ρ). If R becomes 4R and ρ is constant, v_e becomes 4v.
Q2mcq
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.
5t/13
b.
13t/10
c.
13t/5
Correct Answer
d.
10t/13
Step-by-Step AI Explanation
Verified Method
Using Newton's Law of Cooling, -dT/dt = k(T - T_room). Case 1: (90-80)/t = k(85-20) -> 10/t = 65k. Case 2: (80-60)/t2 = k(70-20) -> 20/t2 = 50k. Dividing equations: (10/t)/(20/t2) = 65/50 -> t2/2t = 13/10 -> t2 = 13t/5.
Q2mcq
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.
5t/13
b.
13t/10
c.
13t/5
Correct Answer
d.
10t/13
Step-by-Step AI Explanation
Verified Method
Using Newton's law of cooling: (T1 - T2) / t = k * ((T1 + T2)/2 - Ts). For first case: (90-80)/t = k * (85 - 20) => 10/t = k * 65. For second case: (80-60)/t' = k * (70 - 20) => 20/t' = k * 50. Dividing the two equations: (10/t) / (20/t') = 65/50 => t'/2t = 13/10 => t' = 13t/5.
Q4mcq
Polar molecules are the molecules :
a.
having a permanent electric dipole moment.
Correct Answer
b.
having zero dipole moment.
c.
acquire a dipole moment only in the presence of electric field due to displacement of charges.
d.
acquire a dipole moment only when magnetic field is absent.
Step-by-Step AI Explanation
Verified Method
Polar molecules have centers of positive and negative charge that do not coincide, resulting in a permanent electric dipole moment.
Q4mcq
Polar molecules are the molecules :
a.
having a permanent electric dipole moment.
Correct Answer
b.
having zero dipole moment.
c.
acquire a dipole moment only in the presence of electric field due to displacement of charges.
d.
acquire a dipole moment only when magnetic field is absent.
Step-by-Step AI Explanation
Verified Method
Polar molecules are molecules in which the centres of positive and negative charges do not coincide, leading to a permanent electric dipole moment.
Q6mcq
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 Ad
Correct Answer
b.
(1/2)ε0 E²
c.
ε0 EAd
d.
ε0 E² Ad
Step-by-Step AI Explanation
Verified Method
Energy density (u) = (1/2)ε0 E². Total Energy = u * Volume = (1/2)ε0 E² * Ad.
Q9mcq
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.
No current will flow in p-type, current will only flow in n-type.
b.
current in n-type = current in p-type.
c.
current in p-type > current in n-type.
d.
current in n-type > current in p-type.
Correct Answer
Step-by-Step AI Explanation
Verified Method
Since electron mobility (μe) is greater than hole mobility (μh) in semiconductors, for the same charge carrier concentration and external field, the current in the n-type semiconductor will be greater than in the p-type semiconductor.
Q12mcq
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 :
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) is incorrect but (B) is correct.
b.
(A) and (B) both are correct.
c.
(A) and (B) both are incorrect.
d.
(A) is correct and (B) is incorrect.
Correct Answer
Step-by-Step AI Explanation
Verified Method
Zener diodes act as voltage regulators in reverse bias (breakdown region). The potential barrier for Silicon is ~0.7V and for Germanium is ~0.3V. Statement B is incorrect as it implies all junctions fall in this narrow range.
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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) is incorrect but (B) is correct.
b.
(A) and (B) both are correct.
c.
(A) and (B) both are incorrect.
d.
(A) is correct and (B) is incorrect.
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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.
62 cm
b.
60 cm
c.
21.6 cm
d.
64 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.
62 cm
b.
60 cm
c.
21.6 cm
d.
64 cm
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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 = V0ωC sinωt
b.
Id = V0ωC cosωt
c.
Id = (V0 / ωC) cosωt
d.
Id = (V0 / ωC) sinωt
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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.
10¹⁵
b.
10¹⁸
c.
10¹⁷
d.
10¹⁶
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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) / (2n - 1)
b.
(2n - 1) / (2n)
c.
(2n - 1) / (2n + 1)
d.
(2n + 1) / (2n - 1)
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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.
0.052 cm
b.
0.52 cm
c.
0.026 cm
d.
0.26 cm
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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.
7.0 kW
b.
10.2 kW
c.
8.1 kW
d.
12.3 kW
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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/s²)
a.
7.0 kW
b.
10.2 kW
c.
8.1 kW
d.
12.3 kW
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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.
4 Ω
b.
0.25 Ω
c.
0.5 Ω
d.
1 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.
4 Ω
b.
0.25 Ω
c.
0.5 Ω
d.
1 Ω
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Column - I gives certain physical terms associated with flow of current through a metallic conductor. Column - II gives some mathematical relations involving electrical quantities. Match Column - I and Column - II with appropriate relations.
Column - I: (A) Drift Velocity, (B) Electrical Resistivity, (C) Relaxation Period, (D) Current Density
Column - II: (P) 2m/ne^2τ, (Q) nev_d, (R) eEτ/m, (S) E/J
a.
(A)-(R), (B)-(Q), (C)-(S), (D)-(P)
b.
(A)-(R), (B)-(S), (C)-(P), (D)-(Q)
c.
(A)-(R), (B)-(S), (C)-(Q), (D)-(P)
d.
(A)-(R), (B)-(P), (C)-(S), (D)-(Q)
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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.
216 MeV
b.
0.9 MeV
c.
9.4 MeV
d.
804 MeV
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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.
30
b.
25
c.
15
d.
50
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A particle of mass ‘m’ is projected with a velocity v = kv_e (k < 1) from the surface of the earth. (v_e = escape velocity). The maximum height above the surface reached by the particle is:
a.
(k^2 * R) / (1 - k^2)
b.
(R * k^2) / (1 - k)
c.
(R * k^2) / (1 + k)
d.
(R * k) / (1 + k)
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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.
4 A
b.
0.2 A
c.
0.4 A
d.
2 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/s^2) nearly:
a.
1.4 kg m/s
b.
0 kg m/s
c.
4.2 kg m/s
d.
2.1 kg m/s
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A car starts from rest and accelerates at 5 m/s^2. 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/s^2)
a.
20 sqrt(2) m/s, 10 m/s^2
b.
20 m/s, 5 m/s^2
c.
20 m/s, 0
d.
20 sqrt(2) m/s, 0
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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 plane mirror, it would be a virtual image.
b.
20 cm from the lens, it would be a real image.
c.
30 cm from the lens, it would be a real image.
d.
30 cm from the plane mirror, it would be a virtual image.
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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.
42 rad/s and 58 rad/s
b.
25 rad/s and 75 rad/s
c.
50 rad/s and 25 rad/s
d.
46 rad/s and 54 rad/s
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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.
21.92 cm
b.
219.3 m
c.
219.2 m
d.
2192 m
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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.
21.92 cm
b.
219.3 m
c.
219.2 m
d.
2192 m
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