Explanation

The microscopic form of Ohm's law is:

J = σE

where J is the current density.

σ is the conductivity.

E is the electric field.

Explanation

The frequency heard by the observer as the car approaches is given by the Doppler effect formula:

f' = f * (v / (v - v_s))

where f = 500 Hz, v = 340 m/s, and v_s = 20 m/s.

f' = 500 * (340 / (340 - 20))

= 500 * (340 / 320)

= 500 * 1.0625

= 531.25 Hz

Explanation

The relativistic length contraction formula is:

L = L₀√(1 - v²/c²)

Given L = L₀/2:

L₀/2 = L₀√(1 - v²/c²)

1/2 = √(1 - v²/c²)

1/4 = 1 - v²/c²

v²/c² = 3/4

v = √(3/4) * c = √3/2 * c

The answer is v = √3/2c.

Explanation

Let's denote the mass and radius of both objects as M and R, respectively.

For a thin-walled cylinder about its central axis, I_cylinder = MR².

For a solid sphere about its diameter, I_sphere = (2/5)MR².

The ratio is I_cylinder / I_sphere = MR² / ((2/5)MR²) = 5/2.

Explanation

After 3 half-lives, the mass remaining is calculated as:

Mass remaining = Initial mass / 2³

= 160 μg / 8

= 20 μg

Explanation

A D.C. generator uses split rings (commutator) to reverse the current direction in the coil every half rotation.

This ensures that the output current flows in one direction (direct current).

Explanation

Two parallel conductors carrying current in the same direction attract each other due to magnetic fields they produce.

If currents flow in opposite directions, the force would be repulsive.

Explanation

Magnetic flux linked (Φ) is proportional to the number of turns in the coil.

Doubling the number of turns doubles the total flux linked, assuming the magnetic field and area remain the same.

Explanation

The absorption of X-rays in a given material follows an exponential curve, described by the Beer-Lambert law:

I(x) = I₀ × e^(-μx)

where I(x) is the intensity of the X-rays after passing through a thickness x of the material, I₀ is the initial intensity, μ is the linear attenuation coefficient, and x is the thickness of the material.

Explanation

Given the object's speed is 8 m/s after 1 second, we can determine the acceleration due to gravity on this planet is 8 m/s², since it starts from rest (0 m/s).

To find the speed after 3 seconds, we use the formula: speed = initial speed + acceleration × time

Initial speed = 0 m/s (since it's dropped)

Acceleration = 8 m/s²

Time = 3 seconds

Speed after 3 seconds = 0 + 8 × 3 = 24 m/s