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Physics NEET MCQ
Quiz 1
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Q.1
The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is
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$\pi$
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$\pi/2$
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$.702 \pi$
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0
Explanation
For x = A sin(ωt): velocity v = Aω cos(ωt), acceleration a = −Aω² sin(ωt). Velocity varies as cosine while acceleration varies as (negative) sine — these are 90° (π/2) out of phase with each other.
Q.2
Assertion and Reason (a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I (b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I (c) Statement I is true, Statement II is false (d) Statement I is False, Statement II is True STATEMENT 1:Frequency of oscillation in Simple pendulum depends on Amplitude of oscillation STATEMENT 2:Timeperiod of oscillation in simple pendulum is given by T=2π√L/g
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(a)
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(b)
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(c)
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(d)
Explanation
The defining property of simple harmonic motion (isochronism) is that its period/frequency does NOT depend on amplitude — Statement 1 is false. The standard simple-pendulum period formula T = 2π√(L/g) is correct — Statement 2 is true.
Q.3
The total energy of particle performing SHM depend on
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k, a, m
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k, a
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k, a, x
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k, x
Explanation
Total SHM energy, E = ½mω²A² = ½kA² (using k = mω²), depends on the mass, the force/spring constant, and the amplitude — but not on the instantaneous displacement or time, since it stays constant throughout the motion.
Q.4
Two spring of spring constant a and b are joined in series. The effective spring constant of the combination is given by
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$\sqrt {ab}$
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$\frac {ab}{a+b}$
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$a +b$
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$\frac {a+b}[2}$
Explanation
For springs in series, compliances (1/k) add: 1/k_eff = 1/a + 1/b = (a+b)/(ab) → k_eff = ab/(a+b).
Q.5
Motion of an oscillating liquid column in a U-tube is
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simple harmonic and time-period is directly proportional to the density of the liquid.
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periodic but not simple harmonic.
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periodic but not simple harmonic.
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simple harmonic and time period is independent of the density of the liquid
Explanation
An oscillating liquid column in a U-tube executes SHM with period T = 2π√(L/2g), where L is the total length of the liquid column — density cancels out of this formula entirely (both the oscillating mass and the restoring force scale together with density), so the period is independent of which liquid is used.
Q.6
Assertion and Reason (a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I (b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I (c) Statement I is true, Statement II is false (d) Statement I is False, Statement II is True STATEMENT 1:The quantity F.r where F is force and r is displacement is negative in SHM STATEMENT 2:THe quantity a.r where a is acceleration and r is displacement is positive in SHM
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(a)
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(b)
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(c)
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(d)
Explanation
F = −kx, so F·r = −kx·x = −kx², which is always negative — Statement 1 is true. But acceleration a = −ω²x has exactly the same sign relationship to displacement as force does (since F = ma, with mass always positive), so a·r = −ω²x·x = −ω²x² is ALSO always negative, not positive — Statement 2 is false.
Q.7
Pendulum after some time becomes slow in motion and finally stops due to
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earth’s gravity
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mass of pendulum
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air friction
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None of these
Explanation
A real pendulum gradually loses energy to air resistance (drag) as it swings, causing its amplitude to shrink over time until it eventually comes to rest.
Q.8
Total energy of mass spring system in harmonic motion is E=1/2(mω2A2). Consider another system executing SHM with same amplitude having value of spring constant as half the previous one and mass twice as that of previous one. The energy of second oscillator will be
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E
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2E
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$\sqrt {2} E$
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E/2
Explanation
Using E = ½kA² (k = spring constant, same amplitude A in both cases): the new system has k' = k/2, so E' = ½(k/2)A² = ½ × (½kA²) = E/2. (This holds regardless of the mass change, since E = ½kA² doesn't explicitly depend on mass once k is fixed — though the new mass and k together consistently give the same halved energy either way.)
Q.9
A particle under the action of a SHM has a period of 3 seconds and under the effect of another it has a period 4 seconds. What will be its period under the combined action of both the SHM’s in the same direction?
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7 seconds
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1 sec
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5 sec
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2.4 sec
Explanation
Using the combination f = √(f₁² + f₂²) with f₁ = 1/3 Hz and f₂ = 1/4 Hz: f = √[(1/3)² + (1/4)²] = √(1/9 + 1/16) = √(25/144) = 5/12 Hz T = 1/f = 12/5 = 2.4 s.
Q.10
Angular frequency of system executing SHM depends on a. mass b. total energy c. Force constant d. Amplitude
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Both (a) and (c)
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(a) only
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Both (a) and (d)
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(b) only
Explanation
Angular frequency for a spring-mass system is ω = √(k/m) — it depends only on the mass and the force constant, not on the amplitude or the total energy of oscillation (a bigger swing at the same k and m still completes each cycle in the same time).
Q.11
Four statement are made about SHM (i) Maximum value of velocity in SHM is A2ω (ii) In SHM velocity of the particle is maximum when displacement is maximum (iii) Velocity of the particle is zero in SHM when displacement attains its maximum on either side (iv) Velocity in SHM vary periodically with time Which of these is correct?
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(i) and (iv) only
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(iii) and (iv) only
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(i) and (iii) only
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All correct
Explanation
(i) is wrong — maximum velocity in SHM is Aω, not A²ω. (ii) is wrong — velocity is actually MAXIMUM when displacement is ZERO (at the mean position), not when displacement is maximum. (iii) is correct — velocity IS zero at the extreme positions, where the particle momentarily stops before reversing. (iv) is correct — velocity, given by v = Aω cos(ωt+φ), clearly varies periodically with time. So only (iii) and (iv) are correct.
Q.12
A spring of force constant k is cut into two pieces such that one piece is four times the length of the other. the longer piece will have force constant equal to
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4k/5
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5k/4
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3k/2
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4k
Explanation
Spring constant is inversely proportional to length — cutting a spring into pieces makes each piece stiffer in proportion to how much shorter it is. Splitting the spring in a 1:4 length ratio gives pieces of length L/5 and 4L/5. For the longer piece (4L/5, i.e. 4/5 of the original length): k_longer = k / (4/5) = 5k/4.
Q.13
A particle of mass m is attached to a massless string of length L and is oscillating in vertical plane with one end of string fixed to rigid support. Tension in the string at a certain instant is T=kmg.Then
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K can never be equal to 1
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K can never be greater than 1
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K can never be greater than 3
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K can never be less than 1
Explanation
For a pendulum swinging in a vertical plane, tension is smallest near the extreme points (where speed momentarily drops to zero) and largest at the lowest point of the swing, where it must support gravity AND supply the centripetal force. For the largest possible swing (released from horizontal), the maximum tension works out to 3mg — so tension can range up to (but never past) 3 times mg. (The correct classical result is that K can never be greater than 3, matching the standard pendulum-tension derivation — not "never greater than 1", which the source data marks as correct but doesn't match this well-known result.)
Q.14
Assertion and Reason (a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I (b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I (c) Statement I is true, Statement II is false (d) Statement I is False, Statement II is True STATEMENT 1:The amplitude or energy is defined by the initial position and initial velocity in SHM STATEMENT 2:THe phase of motion is determined by the initial position and initial velocity in SHM
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(a)
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(b)
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(c)
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(d)
Explanation
Both statements are individually true — the amplitude (and hence total energy) of an SHM is determined by the initial position and velocity together, and separately, so is the initial phase. But these are two independent facts about how initial conditions map onto different SHM parameters — Statement 2 doesn't explain WHY Statement 1 is true; they're parallel conclusions, not a cause-and-effect pair.
Q.15
A block is resting on a piston, which is moving vertically with SHM of period 10 seconds. At what amplitude of motion will the block and piston separate?
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.2 m
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0.35 m
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0.45 m
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0.25 m
Explanation
(This works out cleanly if the period is 1 second rather than 10 — likely a scraping typo — combined with the common textbook approximation g ≈ π² m/s².) The block separates from the piston exactly when the piston's maximum downward acceleration equals g (beyond that point, the required normal force would have to go negative, which is impossible): ω²A = g → A = g/ω² With T = 1 s: ω = 2π/T = 2π, so ω² = 4π². A = π²/4π² = 1/4 = 0.25 m.
Q.16
The displacement of a particle is represented by the equation $y = 3 cos ( \frac {\pi}{4} -2 \omega t)$ The motion of the particle is
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simple harmonic with period $\frac {2 \pi}{\omega}$
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periodic but not simple harmonic.
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non-periodic.
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simple harmonic with period $\frac { \pi}{\omega}$
Explanation
y = 3cos(π/4 − 2ωt) is a cosine function, so it's simple harmonic. The coefficient of t inside the cosine (its angular frequency) has magnitude 2ω, giving a period of T = 2π/(2ω) = π/ω.
Q.17
Two SHM’s are respectively represented by $y = a sin( \omega t - kx)$ and $y = bcos (\omega t − kx)$.The phase difference between the two is
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$\frac {\pi}{4}$
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$\frac {3\pi}{4}$
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$\frac {\pi}{2}$
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$\frac {\pi}{6}$
Explanation
cos(θ) = sin(θ + π/2), so y₂ = b cos(ωt−kx) = b sin(ωt−kx+π/2). Comparing phases: y₁ has phase (ωt−kx), y₂ has phase (ωt−kx+π/2) — a difference of π/2.
Q.18
The amplitude and phase of a particle executing SHM depends on
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The displacement of particle at t=0
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The velocity of particle at t=0
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Both Velocity and displacement at t=0
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Neither velocity and displacement at t=0
Explanation
Both the amplitude and the initial phase of an SHM are determined together by the particle's position AND velocity at t = 0 — knowing only one of the two isn't enough to pin down both A and φ.
Q.19
Assertion and Reason (a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I (b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I (c) Statement I is true, Statement II is false (d) Statement I is False, Statement II is True STATEMENT 1:Total energy remains constant in SHM STATEMENT 2:KE is maximum at mean position
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(a)
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(b)
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(c)
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(d)
Explanation
Total energy staying constant in SHM (Statement 1) follows from the restoring force being conservative — energy just trades between kinetic and potential forms without being lost. Kinetic energy being maximum at the mean position (Statement 2) is a true, separate fact about how that fixed total energy is distributed along the motion, but it doesn't itself explain why the TOTAL stays constant — so both are true, but Statement 2 isn't the correct explanation of Statement 1.
Q.20
A particle is executing SHM at midpoint of mean position and extreme position . What is it's KE in terms of total energy E.
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E/2
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4E/3
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$\sqrt {2}E$
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3E/4
Explanation
At the midpoint between mean and extreme position, displacement x = A/2. KE = ½k(A² − x²) = ½k(A² − A²/4) = ½k(3A²/4) = (3/8)kA² Total energy E = ½kA² KE/E = (3/8)/(1/2) = 3/4 → KE = 3E/4.
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