When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L + l). The elastic potential energy stored in the extended wire is:
a.
Mgl
b.
MgL
c.
1/2 Mgl
Correct Answer
d.
1/2 MgL
Step-by-Step AI Explanation
Verified Method
For a wire extended by l under a constant load Mg, elastic potential energy stored = 1/2 × force × extension = 1/2 Mgl.
Q2mcq
A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:
a.
the mass is at the highest point
b.
the wire is horizontal
c.
the mass is at the lowest point
Correct Answer
d.
inclined at an angle of 60° from vertical
Step-by-Step AI Explanation
Verified Method
Tension in the wire is maximum at the lowest point because it must provide centripetal force and also support the weight mg.
Q3mcq
Ionized hydrogen atoms and α-particles with same momenta enter perpendicular to a constant magnetic field B. The ratio of their radii of paths r_H : r_α will be:
a.
2 : 1
Correct Answer
b.
1 : 2
c.
4 : 1
d.
1 : 4
Step-by-Step AI Explanation
Verified Method
For motion in a magnetic field, r = p/(qB). Same momentum means radius is inversely proportional to charge. H+ has charge e and α-particle has charge 2e, so r_H:r_α = 2:1.
Q4mcq
Body A of mass 4m moving with speed u collides with another body B of mass 2m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body A is:
a.
1/9
Correct Answer
b.
8/9
c.
4/9
d.
5/9
Step-by-Step AI Explanation
Verified Method
In an elastic collision total kinetic energy is conserved. The question asks fraction of energy lost by body A, i.e. its own kinetic energy decrease. For m1=4m, m2=2m, initial KE of A = 2mu^2 and final velocity of A = (4m-2m)/(6m)u = u/3. Final KE of A = 2m(u^2/9), so loss fraction = 1 - 1/9 = 8/9? However NEET wording here typically means loss of the colliding body's initial kinetic energy that is transferred away in the collision. The options indicate the intended quantity is the fraction of A's initial energy lost, which is 8/9.
Q5mcq
In a double slit experiment, when light of wavelength 400 nm was used, the angular width of the first minima formed on a screen placed 1 m away, was found to be 0.2°. What will be the angular width of the first minima, if the entire experimental apparatus is immersed in water? (μ_water = 4/3)
a.
0.266°
b.
0.15°
Correct Answer
c.
0.05°
d.
0.1°
Step-by-Step AI Explanation
Verified Method
In a medium, wavelength becomes λ/μ, so angular width of minima decreases by factor μ. Hence 0.2° × 3/4 = 0.15°.
Q6mcq
In which of the following devices, the eddy current effect is not used?
a.
Induction furnace
b.
Magnetic braking in train
c.
Electromagnet
Correct Answer
d.
Electric heater
Step-by-Step AI Explanation
Verified Method
Eddy currents are used in induction furnace and magnetic braking. An electromagnet works due to magnetic field produced by current in a coil, not eddy currents.
Q7mcq
A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 × 10^-2 N/m. The pressure inside the bubble equals pressure at a point Z_0 below the free surface of water in a container. Taking g = 10 m/s^2, density of water = 10^3 kg/m^3, the value of Z_0 is:
a.
100 cm
b.
10 cm
c.
1 cm
Correct Answer
d.
0.5 cm
Step-by-Step AI Explanation
Verified Method
Excess pressure inside soap bubble = 4T/r = 4×2.5×10^-2 / 10^-3 = 100 Pa. This equals hydrostatic pressure ρgh = 1000×10×h, so h = 0.01 m = 1 cm.
Q8mcq
Which colour of the light has the longest wavelength?
a.
Red
Correct Answer
b.
Blue
c.
Green
d.
Violet
Step-by-Step AI Explanation
Verified Method
In the visible spectrum, red has the longest wavelength and violet the shortest.
Q9mcq
A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it?
a.
3 J
b.
30 kJ
c.
2 J
d.
1 J
Correct Answer
Step-by-Step AI Explanation
Verified Method
For a rolling disc, total kinetic energy = translational + rotational = 1/2 mv^2 + 1/2 Iω^2. For a disc, I = 1/2 mR^2 and ω = v/R, so KE = 3/4 mv^2 = 3/4 × 100 × (0.2)^2 = 3 J. The printed options appear inconsistent; the physically correct work needed is 3 J.
Q10mcq
The displacement of a particle executing simple harmonic motion is given by y = A0 + A sin ωt + B cos ωt. Then the amplitude of its oscillation is given by:
a.
√(A0^2 + A^2 + B^2)
b.
√(A^2 + B^2)
Correct Answer
c.
√(A0^2 + (A + B)^2)
d.
A + B
Step-by-Step AI Explanation
Verified Method
The constant term A0 only shifts the mean position and does not affect amplitude. The oscillatory part A sin ωt + B cos ωt has resultant amplitude √(A^2 + B^2).
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The displacement of a particle executing simple harmonic motion is given by y = A_0 + A sin ωt + B cos ωt. Then the amplitude of its oscillation is given by:
a.
√(A0^2 + A^2 + B^2)
b.
√(A^2 + B^2)
c.
√(A0^2 + (A-B)^2)
d.
A + B
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Two similar thin equi-convex lenses, of focal length f each, are kept coaxially in contact with each other such that the focal length of the combination is F1. When the space between the two lenses is filled with glycerin (which has the same refractive index (μ = 1.5) as that of glass), then the equivalent focal length is F2. The ratio F1 : F2 will be:
a.
2 : 1
b.
1 : 2
c.
2 : 3
d.
3 : 4
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Two similar thin equi-convex lenses, of focal length f each, are kept coaxially in contact with each other such that the focal length of the combination is F1. When the space between the two lenses is filled with glycerin (which has the same refractive index, μ = 1.5, as that of glass), the equivalent focal length is F2. The ratio F1 : F2 will be:
a.
2 : 1
b.
1 : 2
c.
2 : 3
d.
3 : 4
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A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of the aluminium rod is: (α_Cu = 1.7 × 10^-5 K^-1 and α_Al = 2.2 × 10^-5 K^-1)
a.
6.8 cm
b.
113.9 cm
c.
88 cm
d.
68 cm
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Six similar bulbs are connected as shown in the figure with a DC source of emf E and zero internal resistance. The ratio of power consumption by the bulbs when (i) all are glowing and (ii) in the situation when two from section A and one from section B are glowing, will be:
a.
4 : 9
b.
9 : 4
c.
1 : 2
d.
2 : 1
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A force F = 20 + 10y acts on a particle in y-direction where F is in newton and y in meter. Work done by this force to move the particle from y = 0 to y = 1 m is
a.
30 J
b.
5 J
c.
25 J
d.
20 J
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In total internal reflection when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be the angle of refraction?
a.
180°
b.
0°
c.
Equal to angle of incidence
d.
90°
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In total internal reflection, when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be the angle of refraction?
a.
180°
b.
0°
c.
Equal to angle of incidence
d.
90°
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When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60° with horizontal, it can travel a distance x1 along the plane. But when the inclination is decreased to 30° and the same object is shot with the same velocity, it can travel a distance x2. Then x1 : x2 will be:
a.
1 : 2
b.
2 : 1
c.
1 : 3
d.
1 : 2√3
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The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by:
a.
30° west
b.
0°
c.
60° west
d.
45° west
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Two particles A and B are moving in uniform circular motion in concentric circles of radii rA and rB with speeds vA and vB respectively. Their time period of revolution is the same. The ratio of angular speed of A to that of B will be:
a.
rA : rB
b.
vA : vB
c.
rB : rA
d.
1 : 1
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A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be: (g = 10 m/s²)
a.
10 rad/s
b.
10π/2 rad/s
c.
10 rad/s
d.
10π rad/s
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Two parallel infinite line charges with linear charge densities +λ C/m and –λ C/m are placed at a distance of 2R in free space. What is the electric field midway between the two line charges?
a.
Zero
b.
λ/(2πϵ0R) N/C
c.
λ/(πϵ0R) N/C
d.
λ/(πϵ02R) N/C
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Two point charges A and B, having charges +Q and –Q respectively, are placed at certain distance apart and force acting between them is F. If 25% charge of A is transferred to B, then force between the charges becomes:
a.
F
b.
9F/16
c.
16F/9
d.
4F/3
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A small hole of area of cross-section 2 mm² is present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m/s², the rate of flow of water through the open hole would be nearly
a.
12.6 × 10^-6 m^3/s
b.
8.9 × 10^-6 m^3/s
c.
2.23 × 10^-6 m^3/s
d.
6.4 × 10^-6 m^3/s
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An 800 turn coil of effective area 0.05 m² is kept perpendicular to a magnetic field 5 × 10^-5 T. When the plane of the coil is rotated by 90° around any of its coplanar axis in 0.1 s, the emf induced in the coil will be:
a.
2 V
b.
0.2 V
c.
2 × 10^-3 V
d.
0.02 V
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An 800-turn coil of effective area 0.05 m² is kept perpendicular to a magnetic field of 5 × 10⁻⁵ T. When the plane of the coil is rotated by 90° around any of its coplanar axis in 0.1 s, the emf induced in the coil will be:
a.
2 V
b.
0.2 V
c.
2 × 10⁻³ V
d.
0.02 V
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The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the figure. The y-projection of the radius vector of rotating particle P is:
a.
y(t) = -3 cos(2πt), where y is in m
b.
y(t) = 4 sin(πt/2), where y is in m
c.
y(t) = 3 cos(3πt/2), where y is in m
d.
y(t) = 3 cos(πt/2), where y is in m
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The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the figure. The y-projection of the radius vector of the rotating particle P is:
a.
y(t) = −3 cos(2πt), where y is in m
b.
y(t) = 4 sin(πt/2), where y is in m
c.
y(t) = 3 cos(3πt/2), where y is in m
d.
y(t) = 3 cos(πt/2), where y is in m
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A parallel plate capacitor of capacitance 20 μF is being charged by a voltage source whose potential is changing at the rate of 3 V/s. The conduction current through the connecting wires, and the displacement current through the plates of the capacitor, would be, respectively.
a.
Zero, 60 μA
b.
60 μA, 60 μA
c.
60 μA, zero
d.
Zero, zero
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In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement of X, where X = A^(1/2) B^(1/3) / C^(2/3) D, will be
a.
13%
b.
16%
c.
-10%
d.
10%
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A cylindrical conductor of radius R is carrying a constant current. The plot of the magnitude of the magnetic field B with the distance d from the centre of the conductor is correctly represented by the figure:
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A gas at 350 K and 15 bar has molar volume 20 percent smaller than that for an ideal gas under the same conditions. The correct option about the gas and its compressibility factor (Z) is:
a.
Z > 1 and attractive forces are dominant
b.
Z > 1 and repulsive forces are dominant
c.
Z < 1 and attractive forces are dominant
d.
Z < 1 and repulsive forces are dominant
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