Polarization possible only for transverse waves (oscillations ⊥ propagation). Longitudinal waves (sound) cannot be polarized. Memory aid: 'Polarization ⇒ transverse nature; light is EM transverse wave'. Wave property frequently tested in competitive exams.
Explanation:
The number of half-lives (n) that have passed is total time / half-life = 15 / 5 = 3 half-lives. The fraction of the sample remaining undecayed is given strictly by the formula (1/2)^n. Therefore, the fraction remaining is (1/2)^3 = 1/2 * 1/2 * 1/2 = 1/8.
Explanation:
From floatation: ρ_wood/ρ_water = fraction submerged in water = 0.6. Thus ρ_wood = 0.6 g/cm³ (since ρ_water = 1 g/cm³). In new liquid (ρ_l = 0.8 g/cm³), fraction submerged f = ρ_wood/ρ_l = 0.6/0.8 = 0.75 = 75%. This uses the principle that fraction submerged equals density ratio. Memory aid: 'f = ρ_object / ρ_fluid'. Such comparative buoyancy problems test application of Archimedes' principle across scenarios, common in competitive exams. Always maintain consistent units (g/cm³ here simplifies calculation).
Assertion (A): The coefficient of volume expansion of a solid is approximately three times its coefficient of linear expansion. Reason (R): Volume is a three-dimensional property derived from cubing the linear dimension.
A.A is false but R is true.
B.Both A and R are true and R is the correct explanation of A.
C.A is true but R is false.
D.Both A and R are true but R is NOT the correct explanation of A.
Explanation:
The coefficient of linear expansion is alpha. A cube of side L has volume V = L^3. When heated, the new length is L(1+alphadT). The new volume is [L(1+alphadT)]^3. Expanding via binomial theorem and ignoring higher-order small terms gives V' = V(1 + 3alphadT). Thus, the volume expansion coefficient gamma is equal to 3alpha. Reason R correctly explains Assertion A.
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