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

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

Mass remaining = Initial mass / 2³

= 160 μg / 8

= 20 μg

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

When an object is placed at the principal focus (F) of a convex lens, the rays emerge parallel after refraction.

Parallel rays appear to meet at infinity, so the image is formed at infinity (very far away).

Explanation

The energy density (u) in a capacitor is given by:

u = ½ε₀E²

Where:

- ε₀ is the permittivity of free space

- E is the electric field intensity between the plates

This shows that the energy density is proportional to the square of the electric field intensity (E²).

Explanation

For a polyatomic gas, Cv is typically 3R, accounting for translational and rotational degrees of freedom.

This value can increase with temperature as vibrational modes become excited, contributing to the specific heat.

Explanation

For projectile motion, two complementary angles θ and 90° - θ give the same range if the initial velocity is constant.

Since 10° + 80° = 90°, the angles 10° and 80° are complementary and will have equal ranges.

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

A quadratic equation has the form ax² + bx + c = 0, and it typically has two roots. 

These roots can be real or complex, and they can be distinct or repeated (in the case of a double root).

Explanation