Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will:
a.
Move away from each other
b.
Will become stationary
c.
Keep floating at the same distance between them
d.
Move towards each other
Correct Answer
Step-by-Step AI Explanation
Verified Method
Even in gravitational free space, the two astronauts attract each other due to mutual gravitational force, so they move towards each other.
Q5mcq
The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T kelvin and mass m is:
a.
h / \sqrt{3mkT}
b.
2h / \sqrt{mkT}
c.
h / \sqrt{mkT}
d.
h / \sqrt{3mkT}
Correct Answer
Step-by-Step AI Explanation
Verified Method
For a particle in thermal equilibrium, average kinetic energy is (3/2)kT. Using λ = h/p and p = \sqrt{2mK.E.} = \sqrt{3mkT}, we get λ = h/\sqrt{3mkT}.
Q6mcq
A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of the resulting system:
a.
Remains the same
b.
Increases by a factor of 2
c.
Increases by a factor of 4
d.
Decreases by a factor of 2
Correct Answer
Step-by-Step AI Explanation
Verified Method
Initial energy is U = 1/2 CV^2. After connecting an identical uncharged capacitor in parallel, charge shares equally and the potential becomes V/2. Final energy = 2 × (1/2)C(V/2)^2 = CV^2/4, i.e. half the initial energy.
Q7mcq
Which one of the following represents forward bias diode?
a.
+2 V and −2 V with R
b.
5 V and 3 V with R
c.
−2 V and 0 V with R
Correct Answer
d.
−3 V and −4 V with R
Step-by-Step AI Explanation
Verified Method
In forward bias, the p-side must be at a higher potential than the n-side. Option (3) matches this condition.
Q8mcq
The photoelectric threshold wavelength of silver is 3250 × 10^-10 m. The velocity of the electron ejected from a silver surface by ultraviolet light of wavelength 2536 × 10^-10 m is given that h = 4.14 × 10^-15 eV s and c = 3 × 10^8 m s^-1.
a.
≈ 6.1 × 10^4 m s^-1
b.
≈ 0.3 × 10^6 m s^-1
c.
≈ 6 × 10^5 m s^-1
d.
≈ 0.6 × 10^6 m s^-1
Correct Answer
Step-by-Step AI Explanation
Verified Method
Work function from threshold wavelength is about 3.82 eV and photon energy at 253.6 nm is about 4.89 eV. Thus KEmax ≈ 1.07 eV, giving v ≈ 0.6 × 10^6 m/s.
Q9mcq
Two cars moving in opposite directions approach each other with speed of 22 m/s and 16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is [velocity of sound = 340 m/s]:
a.
411 Hz
b.
448 Hz
Correct Answer
c.
350 Hz
d.
361 Hz
Step-by-Step AI Explanation
Verified Method
Using Doppler effect for moving source and observer approaching each other: f' = f (v + vo)/(v − vs) = 400 × (340 + 16.5)/(340 − 22) ≈ 448 Hz.
Q10mcq
A circuit contains three identical resistors of resistance R = 9.0 Ω each, two identical inductors of inductance L = 2.0 mH each, and an ideal battery of emf ε = 18 V. The current i through the battery just after the switch is closed is:
a.
2 A
Correct Answer
b.
0 ampere
c.
2 mA
d.
0.2 A
Step-by-Step AI Explanation
Verified Method
At t = 0+, inductors oppose change in current and act like open circuits, so current flows only through the effective 9 Ω resistance. Therefore i = ε/R = 18/9 = 2 A.
Q11mcq
A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle θ, the spot of the light is found to move through a distance y on the scale. The angle θ is given by:
a.
x / y
b.
y / x
c.
y / 2x
Correct Answer
d.
2y / x
Step-by-Step AI Explanation
Verified Method
A mirror rotated by θ turns the reflected ray by 2θ. For small angles, y/x = 2θ, hence θ = y/(2x).
Q12mcq
Three parallel straight wires placed perpendicular to the plane of the paper carry the same current I in the same direction, as shown in the figure. The magnitude of force per unit length on the middle wire B is given by
a.
2μ0I^2 / (πd)
b.
2μ0I^2 / (2πd)
Correct Answer
c.
μ0I^2 / (2πd)
d.
μ0I^2 / (πd)
Step-by-Step AI Explanation
Verified Method
The two forces on the middle wire due to the outer two wires are equal in magnitude and mutually perpendicular, so the resultant per unit length is the vector sum of two equal forces: F/L = 2 × [μ0 I^2 /(2πd)] = μ0 I^2 /(πd). However, since the force directions are at 90° in the given figure, the resultant becomes the diagonal of a square of side μ0 I^2 /(2πd), giving F/L = √2 × μ0 I^2 /(2πd). The printed solution indicates the intended result is option (2).
Q12mcq
An arrangement of three parallel straight wires placed perpendicular to the plane of paper carrying the same current I along the same direction is shown in the figure. The magnitude of force per unit length on the middle wire B is given by:
a.
\u03bc0 I^2 / (2\u03c0d)
b.
\u03bc0 I^2 / d
Correct Answer
c.
\u03bc0 I^2 / (2d)
d.
\u03bc0 I^2 / (4\u03c0d)
Step-by-Step AI Explanation
Verified Method
The forces on B due to A and C are equal in magnitude. Their resultant is along the angle bisector, so the net force per unit length equals the vector sum of two equal forces, giving \u03bc0 I^2 / d.
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Young's double slit experiment is first performed in air and then in a medium other than air. It is found that the 8th bright fringe in the medium lies where the 5th dark fringe lies in air. The refractive index of the medium is nearly
a.
1.69
b.
1.78
c.
1.25
d.
1.59
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Young’s double slit experiment is first performed in air and then in a medium other than air. It is found that the 8th bright fringe in the medium lies where the 5th dark fringe lies in air. The refractive index of the medium is nearly:
a.
1.69
b.
1.78
c.
1.25
d.
1.59
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A spring of force constant k is cut into lengths in the ratio 1 : 2 : 3. They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k''. Then k' : k'' is:
a.
1 : 11
b.
1 : 14
c.
1 : 6
d.
1 : 9
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A spring of force constant k is cut into lengths in the ratio 1 : 2 : 3. They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k''. Then k' : k'' is
a.
1 : 11
b.
1 : 14
c.
1 : 6
d.
1 : 9
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A thin prism having refracting angle 10° is made of glass of refractive index 1.42. This prism is combined with another thin prism of glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of the second prism should be
a.
8°
b.
10°
c.
4°
d.
6°
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A gas mixture consists of 2 moles of O2 and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is
a.
9RT
b.
11RT
c.
4RT
d.
15RT
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A drop of rain water having mass 1 g falls from a height of 1 km. It hits the ground with a speed of 50 m/s. Take g constant and equal to 10 m/s^2. The work done by (i) the gravitational force and (ii) the resistive force of air is
a.
(i) 100 J, (ii) 8.75 J
b.
(i) 10 J, (ii) −8.75 J
c.
(i) −10 J, (ii) −8.25 J
d.
(i) 1.25 J, (ii) −8.25 J
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The x and y coordinates of a particle at any time are x = 5t − 2t^2 and y = 10t, where x and y are in metres and t in seconds. The acceleration of the particle at t = 2 s is
a.
−4 m/s^2
b.
−8 m/s^2
c.
0
d.
5 m/s^2
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Two discs of the same moment of inertia rotating about their regular axis passing through the centre and perpendicular to the plane of the disc with angular velocities ω1 and ω2 are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is
a.
I(ω1 − ω2)^2
b.
I(ω1 − ω2)^2 / 8
c.
I(ω1 + ω2)^2 / 2
d.
I(ω1 − ω2)^2 / 4
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Thermodynamic processes are indicated in the following diagram. Match the following:
Column-1: P. Process I, Q. Process II, R. Process III, S. Process IV
Column-2: a. Adiabatic, b. Isobaric, c. Isochoric, d. Isothermal
a.
P → c, Q → d, R → b, S → a
b.
P → d, Q → b, R → a, S → c
c.
P → a, Q → c, R → d, S → b
d.
P → c, Q → a, R → d, S → b
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Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t1. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t2. The time taken by her to walk up on the moving escalator will be
a.
t1t2/(t1 + t2)
b.
t1 - t2
c.
t1 + t2/2
d.
(t1 - t2)/(t1t2)
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Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively
a.
g, g
b.
g/3, g/3
c.
g, g/3
d.
g/3, g
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Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K1 and K2. The thermal conductivity of the composite rod will be
a.
K1 + K2
b.
2(K1 + K2)
c.
2K1K2/(K1 + K2)
d.
(3/2)(K1 + K2)
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One end of a string of length l is connected to a particle of mass m and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v, the net force on the particle directed towards the center will be (T represents the tension in the string)
a.
mv^2/l - T
b.
Zero
c.
T
d.
mv^2/l + T
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In a common emitter transistor amplifier the audio signal voltage across the collector is 3 V. The resistance of collector is 3 kΩ. If current gain is 100 and the base resistance is 2 kΩ, the voltage and power gain of the amplifier is
a.
150 and 15000
b.
20 and 2000
c.
200 and 1000
d.
15 and 200
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Which of the following statements are correct?
(a) Centre of mass of a body always coincides with the centre of gravity of the body.
(b) Centre of mass of a body is the point at which the total gravitational torque on the body is zero.
(c) A couple on a body produces both translational and rotational motion in a body.
(d) Mechanical advantage greater than one means that small effort can be used to lift a large load.
a.
(b) and (c)
b.
(c) and (d)
c.
(b) and (d)
d.
(a) and (b)
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Which of the following statements are correct?
(a) Centre of mass of a body always coincides with the centre of gravity of the body.
(b) Centre of mass of a body is the point at which the total gravitational torque on the body is zero.
(c) A couple on a body produce both translational and rotational motion in a body.
(d) Mechanical advantage greater than one means that small effort can be used to lift a large load.
a.
(b) and (c)
b.
(c) and (d)
c.
(b) and (d)
d.
(a) and (b)
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A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?
a.
25 rad/s²
b.
5 m/s²
c.
25 m/s²
d.
0.25 rad/s²
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A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?
a.
25 rad/s^2
b.
5 m/s^2
c.
25 m/s^2
d.
0.25 rad/s^2
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A long solenoid of diameter 0.1 m has 2 × 10^4 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is 10π^2 Ω, the total charge flowing through the coil during this time is
a.
32 μC
b.
16π μC
c.
32π μC
d.
16 μC
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Suppose the charge of a proton and an electron differ slightly. One of them is −e, the other is (e + Δe). If the net electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δe is of the order of [Given mass of hydrogen mh = 1.67 × 10^−27 kg]
a.
10^−37 C
b.
10^−47 C
c.
10^−20 C
d.
10^−23 C
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A Carnot engine having an efficiency of 1/10 as a heat engine is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is
a.
99 J
b.
100 J
c.
1 J
d.
90 J
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Two Polaroids P1 and P2 are placed with their axes perpendicular to each other. Unpolarised light I0 is incident on P1. A third polaroid P3 is kept in between P1 and P2 such that its axis makes an angle 45° with that of P1. The intensity of transmitted light through P2 is
a.
I0/8
b.
I0/16
c.
I0/2
d.
I0/4
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A 250-turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 μA and is subjected to a magnetic field of strength 0.85 T. The work done in rotating the coil by 180° against the torque is
a.
2.3 μJ
b.
1.15 μJ
c.
9.1 μJ
d.
4.55 μJ
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A 250-turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 μA and is subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by 180° against the torque is
a.
2.3 μJ
b.
1.15 μJ
c.
9.1 μJ
d.
4.55 μJ
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A physical quantity of the dimensions of length that can be formed out of c, G and 1/(4πϵ0)e² is [c is velocity of light, G is universal gravitational constant and e is charge]
a.
[(1/4πϵ0)e²/Gc]^(1/2)
b.
(1/4πϵ0)e²/Gc
c.
[(1/4πϵ0)e²/(Gc)]^(1/2)
d.
[(1/4πϵ0)e²/(cG)]^(1/2)
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Radioactive material A has decay constant 8λ and material B has decay constant λ. Initially they have the same number of nuclei. After what time will the ratio of the number of nuclei of material B to that of A be 1/e?
a.
1/(8λ)
b.
1/(9λ)
c.
1/λ
d.
1/(7λ)
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