Which of the following pairs of physical quantities has the same dimensions? MCQ with Answer and Explanation

Explanation:
h = ½gt² ⇒ t ∝ √h. If h' = 4h, t' = √4 × t = 2t. Time doubles when height quadruples. Memory aid: 'Free fall: t ∝ √h; 4× height ⇒ 2× time'. Kinematics proportionality frequently tested in competitive exams.

Explanation:
J. J. Thomson measured the specific charge (e/m) of electrons in 1897 using cathode ray tube experiments with electric and magnetic fields. Millikan later measured the charge e (oil drop experiment), allowing mass calculation. Rutherford discovered nucleus; Bohr developed atomic model. Memory aid: 'Thomson = e/m; Millikan = e'. This history-based question tests knowledge of experimental physics milestones, frequently appearing in competitive exams. Always link scientists to their specific measurements: Thomson (e/m), Millikan (e), Chadwick (neutron).

Explanation:
v = √(gR) = √(10×6400×10³) = √(64×10⁶) = 8×10³ m/s = 8 km/s. Escape velocity 11.2 km/s.