PH | MCQs

Explanation

When a spherical ball rolls without slipping:

Total energy (E) = Kinetic energy (K) + Rotational energy (U)

K = (1/2)mv^2

U = (1/2)Iω^2 = (1/5)mv^2 (for a sphere)

E = K + U = (1/2)mv^2 + (1/5)mv^2 = (7/10)mv^2

Fraction of energy associated with rotation:

U/E = ((1/5)mv^2) / ((7/10)mv^2) = 2/7

Explanation

Energy of one photon (E) = hc / λ

h = 6.626 × 10^-34 Js

c = 3 × 10^8 m/s

λ = 4961 Å = 4961 × 10^-10 m

E = (6.626 × 10^-34 Js × 3 × 10^8 m/s) / (4961 × 10^-10 m)

= 4.007 × 10^-19 J

Number of photons required to do 1 J of work:

n = 1 J / (4.007 × 10^-19 J)

= 2.4961 × 10^18

Explanation

Total mechanical energy (E) = (1/2) × m × ω^2 × A^2

ω = 2π / T = 2π / 0.20 s = 10π rad/s

m = 40 g = 0.04 kg

A = 2.0 cm = 0.02 m

E = (1/2) × 0.04 kg × (10π rad/s)^2 × (0.02 m)^2

= 8.0 × 10^-3 J

Explanation

Using the Heisenberg Uncertainty Principle:

ΔE * Δt >= h/4π

where ΔE = h * Δv (energy uncertainty) and Δt = 10^(-8) s (lifetime)

h * Δv * 10^(-8) >= h/4π

Δv >= 1/(4π * 10^(-8))

≈ 8 x 10^6 Hz

Explanation

Pressure is typically measured in units of force per unit area.

In the Imperial system, pressure is commonly measured in Pounds per Square Inch (PSI).

This is a widely used unit of pressure in engineering, physics, and many other fields.

Other common units of pressure include:

• Atmospheres (atm)
• Bars
• Pascals (Pa)
• Torr

Explanation

A free-falling object near Earth's surface accelerates at approximately 9.80 m/s² due to gravity.

This is known as the acceleration due to gravity (g).

Explanation

λ (lambda) is indeed the decay constant. 

The decay constant, λ "lambda", the reciprocal of the mean lifetime (in s−1), sometimes referred to as simply decay rate
The mean lifetime, τ "tau", is the average lifetime (1/e life) of a radioactive particle before decay.

These are related as follows:

Explanation

The momentum 

𝑝 of a photon is given by the equation:

𝑝=ℎ/𝜆 

where:

h is Planck's constant,

λ is the wavelength of the photon.

Since photons are massless, their momentum is not related to mass but to their wavelength.

Explanation

• Energy is measured in Joules (not Newtons).
• Force is measured in Newtons (not Joules).
• Velocity is measured in meters per second (m/s), not meters per second squared (m/s²), which is a unit of acceleration.

Explanation

The moment of inertia depends on the mass of the object,

how the mass is distributed relative to the axis of rotation,

and the axis of rotation itself,

but it does not depend on the angular velocity.