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Jee Main Advanced Physics Chapter Wise Mock Test
Quiz 4
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Q.1
Find the potential of point of a and b when switch S is closed
0%
4V, 12 V
0%
8 V, 8 V
0%
2 V, 2V
0%
4 V, 4V
Explanation
Solution:
Closing the switch ties points a and b together electrically -- by definition they MUST end up at the same potential (a closed switch is just a wire). Since the capacitor branch still carries no steady-state current, the resistor divider is undisturbed, so a=b=8V, the same value the resistors alone set.
Q.2
How much charge flows through the switch S after it is closed?
0%
2.76 μF
0%
7.76 μF
0%
5.76 μF
0%
10 μF
Explanation
Solution:
Before closing: each capacitor holds 3.84μC (from the previous part), giving the node between them (call its net stored charge) zero net charge overall (its two adjoining plates carry +3.84μC and -3.84μC, cancelling).
After closing (node now fixed at 8V): the top capacitor (24V to 8V, i.e. 16V across it) holds 0.48×16=7.68μC, and the bottom one (8V to 0V) holds 0.24×8=1.92μC -- net charge at that node becomes -7.68+1.92=-5.76μC.
The charge that had to flow through the switch to cause this change is the difference: |-5.76-0| = 5.76μC.
Q.3
A point charge q is located at (2, 3, 3) in xyz coordinate. Find the potential differences between A and B A = (2, 3, 3) B = (-2, 3, 3)
0%
$\frac {q}{ 4 \pi \epsilon _0}$
0%
$\frac {q}{ 16 \pi \epsilon _0}$
0%
$\frac {3q}{ 16 \pi \epsilon _0}$
0%
$\frac {q}{ 8 \pi \epsilon _0}$
Explanation
Solution:
Potential difference between two points due to a point charge is kq×(1/r
A
- 1/r
B
), where r
A
and r
B
are each point's distance from the charge -- the general method here, though the exact distances implied by the given coordinates would need to be confirmed against the original figure to pin down the precise numeric factor.
Q.4
A square loop of side L, Mass M and total resistance R falls vertically into uniform magnetic field B directed perpendicular to the plane of the coil. The height h through which the loop falls so that it attain terminal velocity on entering the region of magnetic field
0%
$\frac {MgR^2}{4B^3L^3}$
0%
$\frac {M^2gR^2}{2B^4L^4}$
0%
$\frac {M^2gR^2}{2B^2L^2}$
0%
$\frac {MgR}{2BL}$
Explanation
Solution:
At terminal velocity, the magnetic braking force balances gravity: Mg = BIL = B×(BLv
t
/R)×L = B²L²v
t
/R, so v
t
=MgR/(B²L²).
Reaching that speed by free-fall through height h before entering the field: v
t
²=2gh, so h = v
t
²/(2g) = [MgR/(B²L²)]²/(2g) = M²gR²/(2B⁴L⁴).
Q.5
A bowl of soup rests on a table in the dining car of a Rajdhani train. The acceleration of the train is g/4 in the forward direction. What angle does the surface of the soap make with the horizontal?
0%
$\tan ^{-1} 1/4$
0%
$\tan ^{-1} 4$
0%
$\cos ^{-1} 4$
0%
$\sin ^{-1} 4$
Explanation
Solution:
For a liquid surface in an accelerating container, the surface tilts to angle θ where tanθ=a/g -- here, tanθ = (g/4)/g = 1/4, so θ=tan⁻¹(1/4).
Q.6
Consider the following two statements. (A) Linear momentum of a system of particles is zero. (B) Kinetic energy of system of particles is zero.
0%
A implies B but B does not imply A.
0%
A does not imply B but B implies A.
0%
A implies B and B implies A.
0%
A does not imply B and B does not imply A.
Explanation
Solution:
Zero total momentum does NOT force zero kinetic energy -- two equal masses rushing toward each other at matching speeds have cancelling momenta but plenty of KE. So A does not imply B.
But zero total KE means every single particle has zero speed (kinetic energy is a sum of non-negative terms, so the only way the sum is zero is if each term is), and if everything is at rest, momentum is trivially zero too -- so B does imply A.
Q.7
This question has statement 1 and statementOf the four choices given after the statements, choose the one that best describes the two statements. If two springs S1 and S2 of the force constants k1 and k2 respectively, are stretched by the same force, it is found that more work is done on spring S1 than on spring S2 Statement-l : When stretched by the same amount, work done on S1, will be more than that of S2 Statement-2: k1
0%
Statement I is false and Statement II is true
0%
Statement I is true and Statement II is false
0%
Statement I is true and Statement II is true and statement 2 is the correct explanation of statement 1
0%
Statement I is true and Statement II is true and statement 2 is the not correct explanation of statement 1
Explanation
Solution:
Under the SAME FORCE, extension x=F/k, so the spring with the smaller k stretches further. Work done, W=F²/(2k), is then LARGER for the smaller-k spring -- since S1 received more work under equal force, k
1
<k
2
(Statement 2 is true).
But under the SAME EXTENSION instead, W=½kx² -- now the SMALLER-k spring (S1) would store LESS energy, not more, so Statement 1 (claiming S1 still does more work when stretched by the same amount) is false.
Q.8
Which of the following is correct regarding the first law of thermodynamics ? (i)It is not applicable to any cyclic process (ii)It is a restatement of the principle of conservation of energy (iii)It introduces the concept of the internal energy (iv)It introduces the concept of the entropy
0%
(i) and (iii)
0%
(ii) and (iv)
0%
(i) and (iv)
0%
(ii) and (iii)
Explanation
Solution:
The first law applies just as much to cyclic processes (it's exactly why ΔU=0 over a full cycle) -- so claiming it doesn't apply there is wrong, and entropy is a concept the SECOND law introduces, not the first. What the first law does do is restate energy conservation for thermodynamic systems, and in doing so it defines internal energy U as the state function that makes dQ=dU+dW work.
Q.9
which of the following principles is used in optical fibres?
0%
Total internal reflection
0%
scattering
0%
refraction
0%
Diffraction
Explanation
Solution:
Light entering an optical fibre's core strikes the core-cladding boundary beyond the critical angle every time, reflecting entirely back inward rather than escaping -- total internal reflection is what keeps the light confined and guided along the fibre's length.
Q.10
Two lenses of power- 15 D and +5D are in contact with each other. The focal length of the combination is
0%
+10 cm
0%
+20 cm
0%
-10 cm
0%
-20 cm
Explanation
Solution:
Powers of lenses in contact simply add: P = -15+5 = -10 D.
Focal length f = 1/P = 1/(-10 D) = -0.1 m = -10 cm.
Q.11
This question contains Statement - 1 and Statement -2 Of the four choice given after the Statements , choose the one that best describes the two Statements Statement- 1: Energy is released when heavy undergo fission or light nuclei undergo fusion and Statement- 2: for nuclei , binding energy nucleon increases with increasing Z while for light nuclei it decreases with increasing Z
0%
Statement-1 is true, Statement-2 is false
0%
Statement-1 is false, Statement-2 is true
0%
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1
0%
Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1
Explanation
Solution:
Statement 1 is true -- both heavy-nucleus fission and light-nucleus fusion move toward higher binding energy per nucleon, releasing the difference as energy.
Statement 2 has the trend backwards: binding energy per nucleon actually INCREASES with mass number for light nuclei (climbing toward the peak near iron) and DECREASES with mass number for heavy nuclei beyond that peak -- the opposite of what's claimed here, making statement 2 false.
Q.12
A radioactive nucleus (initial mass number A and atomic number Z) emits 3α-particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be
0%
$\frac {A-Z -4}{Z-2}$
0%
$\frac {A-Z -8}{Z-4}$
0%
$\frac {A-Z -4}{Z-8}$
0%
$\frac {A-Z -12}{Z-4}$
Explanation
Solution:
Each alpha decay drops A by 4 and Z by 2; three of them give ΔA=-12, ΔZ=-6. Each positron (β⁺) decay leaves A unchanged but drops Z by 1; two of them give another ΔZ=-2.
Final: A'=A-12, Z'=Z-8 (protons). Neutrons = A'-Z' = (A-12)-(Z-8) = A-Z-4.
n/p ratio = (A-Z-4)/(Z-8).
Q.13
A signal of 5kHz frequency is amplitude modulated on a carrier wave of frequency 2MHz . The frequency of the resultant signal is /are
0%
2000kHz and 1995kHz
0%
2005kHz. 2000kHz and 1995kHz
0%
2005kHz and 1995kHz
0%
2MHz only
Explanation
Solution:
Standard AM produces three components: the untouched carrier itself (2000 kHz), plus an upper sideband at carrier+signal (2000+5=2005 kHz) and a lower sideband at carrier-signal (2000-5=1995 kHz) -- all three are present in the resultant signal.
Q.14
A uniform string of length 20m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is : (take g=10m/square sec)
0%
2 sec
0%
$\sqrt 2$ s
0%
$2\sqrt 2$ s
0%
$2 \pi \sqrt 2$ s
Explanation
Solution:
Tension at height x above the free (bottom) end equals the weight of string below it, T=μxg, giving a wave speed there of v=√(T/μ)=√(gx) -- independent of the mass per length.
dx/√x = √g dt, and integrating from 0 to L=20m: 2√L = √g·t ⇒ t = 2√(L/g) = 2√(20/10) = 2√2 s.
Q.15
If there were a reduction in gravitational effect, which of the following forces do you think would change in some respect?
0%
Magnetic force
0%
Electrostatic force
0%
Viscous force
0%
Archimedes uplift
Explanation
Solution:
Archimedes' buoyant force is ρVg -- directly proportional to g by its own formula, so any change in gravity changes it immediately. Magnetic, electrostatic, and viscous forces all arise from entirely separate physical mechanisms that don't reference gravitational field strength at all.
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