The electric field outside a spherical charge distribution is given by E = Q/4πε₀r². At 2R, it becomes Q/4πε₀(2R)².

For a spherical shell, the electric field outside the shell behaves as if all the charge were concentrated at the center, so E = Q/(4πε₀R²).

By Gauss's law, the electric field inside a uniformly charged spherical shell is zero.

By Gauss's law, the electric field inside a uniformly charged spherical shell is zero.

The ratio of gold to silver to bronze medals is 1:1:1 since each position gets one medal.

Winning percentage = (wins / total games) × 100 = (8 / (8 + 2)) × 100 = 80%.

Matches won = 70% of 50 = 0.7 * 50 = 35 matches.

Games won = 75% of 40 = 0.75 × 40 = 30 games.

Matches won = 75% of 40 = 0.75 × 40 = 30 matches.

Using Hooke's law, F = kx = 200 N/m * 0.5 m = 100 N.

Using Hooke's law, F = kx = 200 N/m * 0.1 m = 20 N.

Potential Energy (PE) = 1/2 * k * x^2 = 1/2 * 200 N/m * (0.1 m)^2 = 1 J

Potential Energy in spring (PE) = 0.5 × k × x² = 0.5 × 300 N/m × (0.2 m)² = 0.5 × 300 × 0.04 = 6 J.

Potential Energy in Spring (PE) = 1/2 kx^2 = 1/2 * 500 N/m * (0.2 m)^2 = 10 J

Potential Energy (PE) = 0.5 * k * x² = 0.5 * 200 N/m * (0.5 m)² = 25 J.

According to Hooke's law, elongation is inversely proportional to the spring constant; thus, if the spring constant is doubled, the elongation halves.

Using Hooke's Law, F = kx, we have k = F/x = 10 N / 0.1 m = 100 N/m.

Using Hooke's law, k = F/x = 10 N / 0.05 m = 200 N/m.

Potential Energy = 0.5 × k × x² = 0.5 × 200 N/m × (0.1 m)² = 1 J.

Work done = 0.5 × k × x^2 = 0.5 × 200 N/m × (0.1 m)^2 = 1 J.

Potential Energy in spring = 0.5 × k × x² = 0.5 × 200 N/m × (0.5 m)² = 25 J.

Work done = 0.5 × k × x² = 0.5 × 200 N/m × (0.5 m)² = 25 J.

Perimeter of a square = 4 × side. Thus, 40 = 4 × side, giving side = 10 cm. Area = side² = 10² = 100 cm².

Perimeter of a square = 4 × side. Thus, 48 = 4 × side, giving side = 12 cm. Area = side² = 12² = 144 cm².

The perimeter of a square is given by P = 4s, where s is the length of one side. Therefore, 4s = 64 cm, leading to s = 16 cm.

Percentage Increase = ((New Price - Old Price) / Old Price) * 100 = ((100 - 80) / 80) * 100 = 25%.

Using h = (1/2)gt², where h = 20 m and g = 9.8 m/s², we have 20 = (1/2)*9.8*t². Solving gives t² = 4.08, so t ≈ 2 s.

Using h = (1/2)gt², where h = 20 m and g = 9.8 m/s², we have 20 = (1/2)*9.8*t². Solving gives t² = 4.08, so t ≈ 2 s.

Distance fallen (s) = (1/2)gt² = (1/2)(9.8)(2²) = 19.6 m.

Distance fallen (s) = (1/2)gt² = (1/2)(9.8)(3²) = 44.1 m.