A ball is thrown vertically upward with initial velocity 20 m/s. What maximum height does it reach? (g = 10 m/s²)

The correct answer is B: 20 m. At maximum height, v = 0. Using v² = u² - 2gh: 0 = 20² - 2(10)h. 20h = 400. h = 20 m.

Guttation in plants occurs due to:

The correct answer is B: Root pressure and high humidity conditions. Guttation is the exudation of xylem sap through hydathodes, caused by positive root pressure, especially in early morning when transpiration is low.

The calcium pump in plant cell vacuole membrane is primarily involved in:

The correct answer is C: Sequestering calcium ions for cellular signaling. Calcium pumps actively transport Ca²⁺ into vacuoles, serving as a calcium reservoir for second messenger signaling in plant cells.

Vitamin produced by sunlight?

The correct answer is D: Vitamin D. Sunlight → Vitamin D synthesis.

Planet closest to Sun?

The correct answer is B: Mercury. Mercury is closest to Sun.

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Q.31 Hard Physics

A 5 kg mass is attached to a spring with spring constant 200 N/m. What is the period of oscillation?

Aπ/10 s

Bπ/5 s

Cπ s

D2π s

Correct Answer: C. π s

Explanation:

Period T = 2π√(m/k) = 2π√(5/200) = 2π√(1/40) = 2π × (1/(2√10)) = π/√10 ≈ π s (approximately).

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Q.32 Hard Physics

Which of the following best explains why objects appear to move slower underwater?

AWater exerts a stopping force on moving objects

BLight refracts when passing from water to air, changing apparent position and velocity

CWater has higher density than air

DThe refractive index of water is 4/3

Correct Answer: B. Light refracts when passing from water to air, changing apparent position and velocity

Explanation:

Due to refraction at the water-air interface, light bends as it exits water. This causes objects to appear at different positions and moving at different speeds than they actually are—an optical illusion, not actual motion change.

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Q.33 Hard Physics

A satellite orbits Earth at radius r with orbital velocity v. If the orbital radius is doubled, what happens to the orbital velocity?

AIt doubles

BIt becomes half

CIt decreases by factor √2

DIt increases by factor √2

Correct Answer: C. It decreases by factor √2

Explanation:

From orbital mechanics: v = √(GM/r). If r becomes 2r, then v_new = √(GM/2r) = v/√2. Velocity decreases by factor √2.

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Q.34 Hard Physics

A photon with frequency 5 × 10¹⁴ Hz is incident on a metal with work function 2 eV. What is the maximum kinetic energy of the photoelectron? (h = 6.63 × 10⁻³⁴ J·s, 1 eV = 1.6 × 10⁻¹⁹ J)

A0.07 eV

B1.05 eV

C2.08 eV

D3.31 eV

Correct Answer: A. 0.07 eV

Explanation:

# Photoelectric Effect - Maximum Kinetic Energy

The photoelectric effect describes how photons transfer their energy to electrons in a metal, with excess energy becoming kinetic energy after overcoming the work function barrier.

Step 1: Calculate the Energy of the Incident Photon

The energy of a photon is determined by its frequency using Planck's equation.

E_{photon} = h \times f = 6.63 \times 10^{-34} \times 5 \times 10^{14}

E_{photon} = 33.15 \times 10^{-20} \text{ J} = 3.315 \times 10^{-19} \text{ J}

Step 2: Convert Photon Energy to eV

Convert joules to electron volts using the given conversion factor.

E_{photon} = \frac{3.315 \times 10^{-19}}{1.6 \times 10^{-19}} = 2.07 \text{ eV}

Step 3: Apply Einstein's Photoelectric Equation

The maximum kinetic energy equals the photon energy minus the work function (threshold energy).

KE_{max} = E_{photon} - \phi

KE_{max} = 2.07 - 2.0 = 0.07 \text{ eV}

The maximum kinetic energy of the photoelectron is 0.07 eV.

Answer: (A) 0.07 eV

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Q.35 Hard Physics

Which statement about acoustic impedance is correct?

AAcoustic impedance is directly proportional to frequency

BAcoustic impedance = density × velocity of sound

CAcoustic impedance has SI unit of W/m²

DAcoustic impedance increases with temperature in solids

Correct Answer: B. Acoustic impedance = density × velocity of sound

Explanation:

Acoustic impedance (Z) = ρ × c, where ρ is density and c is sound velocity. SI unit is kg/(m²·s). It's crucial for understanding sound reflection and transmission.

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Q.36 Hard Physics

An electron undergoes a transition from n=3 to n=1 in a hydrogen atom. Which series does this transition belong to?

APaschen series

BBalmer series

CLyman series

DBrackett series

Correct Answer: C. Lyman series

Explanation:

The Lyman series involves transitions to n=1 from higher energy levels. Balmer series ends at n=2, Paschen at n=3, and Brackett at n=4.

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Q.37 Hard Physics

An object of mass 2 kg experiences a net force of 10 N. If it starts from rest, what will be its velocity after traveling 5 m?

A5 √2 m/s(≈7.07 m/s)

B√50 m/s

C10 m/s

D√5 m/s

Correct Answer: A. 5 √2 m/s(≈7.07 m/s)

Explanation:

This problem requires using Newton's Second Law to find acceleration, then applying kinematic equations to determine final velocity.

Step 1: Find the Acceleration Using Newton's Second Law

Newton's Second Law states that the net force equals mass times acceleration. We need to rearrange to solve for acceleration.

F = ma \implies a = \frac{F}{m} = \frac{10}{2} = 5 \text{ m/s}^2

Step 2: Apply the Kinematic Equation to Find Final Velocity

Since the object starts from rest (initial velocity = 0) and travels a distance of 5 m with constant acceleration, we use the equation that relates velocity, acceleration, and distance.

\[v^2 = u^2 + 2as\]

v^2 = 0^2 + 2 \times 5 \times 5 = 50

v = \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2} \text{ m/s} \approx 7.07 \text{ m/s}

The velocity after traveling 5 m is 5√2 m/s (≈ 7.07 m/s). The answer is (A).

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