Explanation

Given:

Magnification M = 5

Distance between lenses L = f₀ + fₑ = 24 cm

Magnification formula M = f₀ / fₑ

Let's solve for f₀ and fₑ:

1. f₀ / fₑ = 5 => f₀ = 5fₑ

2. f₀ + fₑ = 24

Substituting f₀ = 5fₑ into the second equation:

5fₑ + fₑ = 24

6fₑ = 24

fₑ = 4 cm

Now, f₀ = 5fₑ = 5 × 4 = 20 cm

Explanation

The equation of continuity A₁V₁ = A₂V₂ represents the conservation of mass in fluid flow.

The constant is equal to the Volume flow rate, which is the volume of fluid passing through a given area per unit time.

Explanation

If the original cable breaks at a stretch of 2 mm, each half will have half the length and thus half the maximum stretch:

Maximum stretch for half = 2 mm / 2 = 1 mm.

Explanation

The energy equivalent of 1 atomic mass unit (a.m.u) is given by Einstein's mass-energy equivalence formula E = mc².

1 a.m.u = 931 MeV/c², so the energy equivalent is 931 MeV.

Explanation

Time = Energy / Power

Given Energy = 1.4 × 10⁶ J and Power = 2 kW = 2000 W:

Time = (1.4 × 10⁶ J) / (2000 W)

Time = 1.4 × 10⁶ / 2000

= 700 s

Explanation

Pressure P = F/A. The uncertainty in P is given by:

(ΔP/P) = (ΔF/F) + (ΔA/A)

Given ΔF/F = 2% and ΔA/A = 5%,

(ΔP/P) = 2% + 5% = 7%

Explanation

When a body moves with uniform velocity, its speed and direction remain constant throughout the motion.

In such a case, the average velocity over any time interval is equal to the instantaneous velocity at any moment.

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.