If the earth suddenly shrinks to half its present radius without any change in its mass, the duration of a day on earth will become: MCQ with Answer and Explanation
If the earth suddenly shrinks to half its present radius without any change in its mass, the duration of a day on earth will become:
A. 6 hours
B. 24 hours
C. 48 hours
D. 12 hours
Answer: Option A
Solution (By JKSSB Mock Tests)
By conservation of angular momentum: I1w1 = I2w2. Moment of inertia of a solid sphere is 2/5 MR^2. So, (R1^2) * (2pi/T1) = (R2^2) * (2pi/T2). If radius halves, R2 = R1/2. R1^2 / T1 = (R1/2)^2 / T2. T2 = T1 / 4. A day is 24 hours, so 24/4 = exactly 6 hours.
Torricelli's Law states that the velocity of efflux of a fluid through a sharp-edged hole at the bottom of a tank filled to a depth 'h' is identical to:
A.The velocity of a sound wave in that fluid.
B.The critical velocity for turbulent flow.
C.The terminal velocity of the fluid.
D.The velocity acquired by a freely falling body dropped from height 'h'.
Explanation:
Torricelli's Law is a direct application of Bernoulli's principle. It proves mathematically that the velocity of fluid exiting a small hole (efflux velocity v) is v = sqrt(2gh). This is exactly the same velocity a solid body would acquire if it fell freely under gravity from rest over the same vertical height 'h'.
Explanation:
Diamagnetic materials have small negative susceptibility (χ ≈ -10⁻⁵), meaning they weakly repel magnetic fields. Paramagnetic: small positive χ; ferromagnetic: large positive χ. This classification is based on response to external magnetic fields. Memory aid: 'Diamagnetic: repelled by magnets; χ < 0'. This conceptual question tests magnetism fundamentals, crucial for competitive exams. Always link susceptibility sign to material behavior: negative χ ⇒ diamagnetic (weak repulsion), positive ⇒ paramagnetic/ferromagnetic (attraction).
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