A solid sphere and a hollow sphere of same mass and radius are rolled down an incline. Which reaches bottom first? MCQ with Answer and Explanation

A solid sphere and a hollow sphere of same mass and radius are rolled down an incline. Which reaches bottom first?
A. Depends on material
B. Both together
C. Solid sphere
D. Hollow sphere
Answer: Option C
Solution (By JKExamLibrary)
Solid sphere has smaller moment of inertia (2/5 MR²) than hollow (2/3 MR²). Less energy in rotation, more in translation, faster.

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Question #1
A wire of resistance R is stretched to double its length. Assuming volume remains constant, the new resistance is:
A. R/2
B. 4R
C. 2R
D. R

Correct Answer: Option B


Explanation:
Resistance R = ρL/A. Volume V = A·L constant. If L' = 2L, then A' = V/L' = V/(2L) = A/2. Thus R' = ρ(2L)/(A/2) = 4(ρL/A) = 4R. Resistance increases by factor of 4. Memory tip: 'Stretching wire: R ∝ L² when volume constant'. This proportional reasoning problem tests resistance concepts, frequently appearing in competitive exams. Always verify volume conservation assumption; if area changed independently, result would differ. This problem assesses understanding of geometric effects on electrical properties.

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Question #2
Which defect of vision is correctly matched with its correcting lens?
A. Hypermetropia - Concave lens
B. Myopia - Concave lens
C. Presbyopia - Cylindrical lens
D. Myopia - Convex lens

Correct Answer: Option B


Explanation:
Myopia (near-sightedness) occurs when the image is focused in front of the retina. It is corrected using a concave (diverging) lens. Hypermetropia (far-sightedness) is corrected with a convex (converging) lens. Astigmatism is corrected with a cylindrical lens. Presbyopia is usually corrected with bifocal lenses.

This question belongs to: Science Physics
Question #3
An object placed at infinity in front of a convex mirror forms image at
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Correct Answer: Option A


Explanation:
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This question belongs to: Science Physics