A wire of resistivity ρ, length L, area A has resistance R. If length doubled and area halved, new resistance is MCQ with Answer and Explanation

Explanation:
Acceleration due to gravity at height h: g' = gR²/(R+h)², where R is Earth's radius. Given h = R, so g' = gR²/(2R)² = gR²/4R² = g/4. This inverse square law dependence arises from Newton's law of gravitation. At depth, variation differs, but for height, this formula applies. Memory aid: Double the distance from center ⇒ gravity becomes one-fourth. This standard result is frequently tested in gravitation sections of competitive exams. Always verify whether height or depth is specified, as formulas differ significantly.

Explanation:
Let distance d, usual time t hours. d/5 = t + 10/60, d/6 = t - 5/60. Subtract: d/5 - d/6 = (15/60) => d/30 = 0.25 => d = 7.5 km. Commonly asked.

Explanation:
Diamonds are cut in such a way that light entering them hits multiple facets from the inside at an angle greater than the critical angle (which is very low for diamond, around 24.4°). This results in multiple total internal reflections, trapping light and forcing it out of specific faces, creating a brilliant sparkle.