What is the rate of change of momentum of a body directly proportional to, according to Newton's Second Law of Motion?
A
The applied net external force
✓ Correct
C
The velocity of the body
D
The gravitational potential
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Step-by-Step Explanation & Concept Rationale
Newton's Second Law states that F = dp/dt (the rate of change of momentum is equal to the net applied force).
A ball is projected horizontally from a height h with initial velocity v. At the same instant, an identical ball is dropped vertically from the same height. Neglecting air resistance, which ball hits the ground first?
A
Both balls hit the ground at exactly the same time
✓ Correct
B
The dropped ball hits first
C
The horizontally projected ball hits first
D
It depends on the mass of the balls
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Step-by-Step Explanation & Concept Rationale
Vertical and horizontal motions are completely independent; both balls experience the identical vertical acceleration g and initial vertical velocity zero, taking time t = sqrt(2h/g).
What is the centripetal acceleration of an object of mass m moving at constant speed v in a circular path of radius r?
A
a = v² / r directed towards the center
✓ Correct
B
a = v / r² directed tangentially
C
a = v² * r directed outward
D
a = zero because speed is constant
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Step-by-Step Explanation & Concept Rationale
Centripetal acceleration is a = v²/r directed radially inward toward the center of rotation.
In an isolated system, what quantities are conserved during a perfectly elastic collision between two particles?
A
Both total linear momentum and total kinetic energy
✓ Correct
B
Only total linear momentum, kinetic energy is lost
C
Only kinetic energy, momentum changes
D
Neither momentum nor kinetic energy
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Step-by-Step Explanation & Concept Rationale
In elastic collisions, both total momentum and total kinetic energy are strictly conserved.
What is the moment of inertia of a uniform solid cylinder of mass M and radius R rotating about its central longitudinal axis?
A
I = (1/2) M R²
✓ Correct
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Step-by-Step Explanation & Concept Rationale
For a solid cylinder or disk of mass M and radius R about its cylindrical axis, I = 1/2 MR².
How much work is done by a centripetal force on a satellite orbiting Earth in a circular orbit?
A
Zero work, because the force is always perpendicular to the displacement vector
✓ Correct
B
Positive work equal to G*M*m/r
C
Negative work equal to kinetic energy
D
Infinite work over infinite revolutions
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Step-by-Step Explanation & Concept Rationale
Work W = F * d * cos(theta). For circular motion, theta = 90 deg, so cos(90) = 0, meaning no work is done.
What fundamental law of physics is represented by Bernoulli's Principle in fluid dynamics?
A
The Law of Conservation of Energy
✓ Correct
B
The Law of Conservation of Momentum
C
The Law of Conservation of Mass
D
The Second Law of Thermodynamics
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Step-by-Step Explanation & Concept Rationale
Bernoulli's equation (P + 1/2 rho*v² + rho*g*h = constant) is a direct formulation of conservation of mechanical energy for steady, incompressible, non-viscous fluid flow.
What happens to the terminal velocity of a small spherical raindrop falling through air if its radius is doubled (Stokes' Law)?
A
It increases by a factor of 4 (quadruples)
✓ Correct
D
It increases by a factor of 8
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Step-by-Step Explanation & Concept Rationale
Terminal velocity v_t is proportional to r² (from equating weight proportional to r³ with viscous drag 6*pi*eta*r*v). Doubling radius increases v_t by 2² = 4.
What is the theoretical maximum efficiency of a Carnot heat engine operating between a hot reservoir at T_H and a cold reservoir at T_C (in Kelvin)?
A
eta = 1 - (T_C / T_H)
✓ Correct
D
eta = (T_H - T_C) / T_C
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Step-by-Step Explanation & Concept Rationale
The Carnot efficiency is the absolute thermodynamic upper limit for any heat engine: eta = (T_H - T_C) / T_H = 1 - T_C/T_H.
In an adiabatic process involving an ideal gas, which thermodynamic variable remains zero?
A
Heat transfer (dQ = 0)
✓ Correct
C
Change in internal energy (dU = 0)
D
Change in temperature (dT = 0)
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Step-by-Step Explanation & Concept Rationale
An adiabatic process is thermally insulated from the surroundings such that no heat enters or leaves the system (Q = 0).
According to the Second Law of Thermodynamics, what happens to the total entropy of an isolated system during an irreversible spontaneous process?
A
It always increases (dS > 0)
✓ Correct
C
It remains strictly constant
D
It fluctuates unpredictably
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Step-by-Step Explanation & Concept Rationale
The Second Law dictates that the entropy of an isolated system never decreases and strictly increases in all natural spontaneous irreversible processes.
What is the time period T of a simple pendulum of length L in a gravitational field g for small angular displacements?
A
T = 2 * pi * sqrt(L / g)
✓ Correct
B
T = 2 * pi * sqrt(g / L)
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Step-by-Step Explanation & Concept Rationale
The period of a simple pendulum is T = 2*pi*sqrt(L/g), independent of the mass of the bob.
When light travels from an optically denser medium (refractive index n1) into a rarer medium (n2) at an angle of incidence greater than the critical angle, what phenomenon occurs?
A
Total Internal Reflection
✓ Correct
B
Polarization by Scattering
D
Refraction towards the normal
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Step-by-Step Explanation & Concept Rationale
Total internal reflection occurs when light strikes a boundary with a rarer medium at an angle exceeding critical angle theta_c = arcsin(n2/n1).
In Young's Double-Slit Experiment, what is the fringe width (fringe spacing beta) on a screen at distance D for light of wavelength lambda with slit separation d?
A
beta = (lambda * D) / d
✓ Correct
B
beta = (lambda * d) / D
C
beta = (d * D) / lambda
D
beta = lambda / (d * D)
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Step-by-Step Explanation & Concept Rationale
Fringe spacing beta = lambda * D / d.
What is Coulomb's law for the electrostatic force between two point charges q1 and q2 separated by distance r in vacuum?
A
F = (1 / (4 * pi * epsilon_0)) * (q1 * q2 / r²)
✓ Correct
B
F = (1 / (4 * pi * epsilon_0)) * (q1 * q2 / r)
C
F = epsilon_0 * (q1 * q2 / r²)
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Step-by-Step Explanation & Concept Rationale
Coulomb's Law states force is directly proportional to the product of charges and inversely proportional to the square of distance.
What is the equivalent capacitance when two capacitors C1 and C2 are connected in parallel?
A
C_eq = C1 + C2
✓ Correct
B
C_eq = (C1 * C2) / (C1 + C2)
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Step-by-Step Explanation & Concept Rationale
In parallel, capacitors add directly: C_eq = C1 + C2.
According to Faraday's Law of Electromagnetic Induction and Lenz's Law, what is the induced electromotive force (EMF)?
A
EMF = - N * (dPhi / dt)
✓ Correct
B
EMF = + N * (dPhi / dt)
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Step-by-Step Explanation & Concept Rationale
Faraday-Lenz Law states induced EMF is proportional to the negative rate of change of magnetic flux through the circuit.
What is the energy E of a photon of light with frequency f according to Planck's Quantum Theory?
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Step-by-Step Explanation & Concept Rationale
Planck's equation states that photon energy is quantized as E = hf, where h is Planck's constant (6.626 x 10^-34 J s).
In the Photoelectric Effect, what happens to the maximum kinetic energy of emitted photoelectrons when the frequency of incident light is increased above the threshold frequency?
A
It increases linearly with incident frequency
✓ Correct
B
It remains constant while electron count increases
C
It decreases exponentially
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Step-by-Step Explanation & Concept Rationale
Einstein's photoelectric equation (KE_max = hf - Phi) shows that kinetic energy increases linearly with photon frequency.
What is the half-life t_1/2 of a radioactive isotope with decay constant lambda?
A
t_1/2 = ln(2) / lambda ≈ 0.693 / lambda
✓ Correct
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Step-by-Step Explanation & Concept Rationale
Half-life is related to the decay constant by t_1/2 = ln(2)/lambda = 0.693/lambda.
What is the de Broglie wavelength lambda associated with a particle of mass m moving with velocity v?
A
lambda = h / (m * v) = h / p
✓ Correct
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Step-by-Step Explanation & Concept Rationale
The de Broglie wave equation relates matter wavelength to momentum via lambda = h/p.
What is the SI unit of Magnetic Flux?
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Step-by-Step Explanation & Concept Rationale
Magnetic flux is measured in Webers (Wb = T m²). Magnetic flux density is measured in Tesla (T).
What is the SI unit of Self-Inductance and Mutual Inductance?
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Step-by-Step Explanation & Concept Rationale
Inductance is measured in Henries (1 H = 1 Wb/A = 1 V s/A).
What type of semiconductor is formed when pure silicon (Group IV) is doped with a trivalent impurity like Boron or Gallium?
A
p-type semiconductor (holes are majority carriers)
✓ Correct
B
n-type semiconductor (electrons are majority carriers)
C
Intrinsic semiconductor
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Step-by-Step Explanation & Concept Rationale
Trivalent dopants have 3 valence electrons, creating electron vacancies (holes), producing p-type semiconductors.
What type of semiconductor is produced by doping Germanium or Silicon with a pentavalent impurity like Phosphorus or Arsenic?
A
n-type semiconductor (free electrons are majority carriers)
✓ Correct
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Step-by-Step Explanation & Concept Rationale
Pentavalent dopants donate an extra free conduction electron, producing n-type semiconductors.