Which of the following prefix represents 10⁻¹⁵? MCQ with Answer and Explanation

Explanation:
For resistors in parallel, the reciprocal of the equivalent resistance (1/Rp) is the sum of the reciprocals of individual resistances. 1/Rp = 1/R1 + 1/R2 + 1/R3 = 1/2 + 1/3 + 1/6. Finding a common denominator (6): 1/Rp = 3/6 + 2/6 + 1/6 = 6/6 = 1. Therefore, Rp = 1 Ω.

Explanation:
J. J. Thomson discovered the electron in 1897 through cathode ray tube experiments, measuring charge-to-mass ratio (e/m) of cathode rays. Proton: Rutherford; neutron: Chadwick; nucleus: Rutherford's gold foil experiment. Memory aid: 'Thomson = plum pudding model (electrons in positive sphere)'. This historical question tests knowledge of subatomic particle discoveries, frequently examined in competitive exams. Always recall the experimental methods: Thomson (cathode rays), Millikan (oil drop for e), Rutherford (alpha scattering).

Explanation:
The gravitational potential V inside a uniform solid sphere at a distance r from the center is V = -GM * (3R^2 - r^2) / (2R^3). At the exact center of the Earth, r = 0. Substituting r = 0 gives V = -GM(3R^2) / 2R^3 = -3GM / 2R. The potential is strictly non-zero and highly negative.