A block of wood floats in water with 60% of its volume submerged. In a liquid of density 0.8 g/cm³, the fraction of volume submerged will be: MCQ with Answer and Explanation
A block of wood floats in water with 60% of its volume submerged. In a liquid of density 0.8 g/cm³, the fraction of volume submerged will be:
A. 48%
B. 60%
C. 80%
D. 75%
Answer: Option D
Solution (By JKSSB Mock Tests)
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).
Explanation:
The angle of dip is the angle the Earth's total magnetic field vector makes with the horizontal surface. At the magnetic equator, the magnetic field lines are perfectly parallel to the ground (0 degrees). At the magnetic poles, the field lines plunge strictly vertically downward (or upward) into the ground, making a 90-degree angle with the horizontal.
Explanation:
Pendulum period T = 2π√(l/g) for small amplitudes. It depends on length l and gravity g, but not on bob mass or amplitude (isochronism for small angles). Mass independence arises because gravitational force and inertia both proportional to mass, canceling out. Memory aid: 'Pendulum: T ∝ √(l/g); independent of mass and small-amplitude'. This conceptual question tests oscillations fundamentals, frequently examined in competitive exams. Always verify the small-angle approximation; competitive exams assume it unless specified otherwise. This problem assesses understanding of which parameters affect periodic motion.
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