Which of the following pairs of physical quantities has the same dimensions?
A. Force and Power
B. Angular Momentum and Planck's Constant
C. Pressure and Strain
D. Momentum and Kinetic Energy
Answer: Option B
Solution (By JKSSB Mock Tests)
Angular momentum (L = mvr) has dimensions [ML²T⁻¹]. Planck's constant (h = E/ν) also has dimensions [ML²T⁻¹]. They share the same dimensional formula. Force is [MLT⁻²], Power is [ML²T⁻³], Momentum is [MLT⁻¹], and Strain is a dimensionless quantity [M⁰L⁰T⁰]. This is a frequent exam question.
Explanation:
g' = g (R/(R+h))². If h=R, g' = g (R/2R)² = g/4. Weight = mg' = mg/4, one-fourth. Above surface, g decreases with square of distance from centre.
Explanation:
Electric generators convert mechanical energy to electrical energy using electromagnetic induction: rotating a coil in magnetic field (or vice versa) induces EMF due to changing magnetic flux. This is Faraday's law application. Motors use the reverse principle (force on current-carrying conductor in field). Memory tip: 'Generator: motion ⇒ electricity (induction); Motor: electricity ⇒ motion (force)'. This application question tests understanding of device principles, common in competitive exams. Always distinguish generator (induction) from motor (Lorentz force) operation.
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