Q.

Imagine a hole drilled along the radius of earth. A uniform rod of length equal to radius (R) of earth is inserted into the hole. The distance of centre of gravity of the rod from the centre of earth is mnR, where m and n are positive integers and co-primes. Find the value of m + n.

Moderate

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By Expert Faculty of Sri Chaitanya

answer is 5.

(Detailed Solution Below)

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Detailed Solution

ycg=∫ yg'dm∫ g'dm=∫0RyλdygRy∫0RλdygRy=λgR∫0Ry2dyλgR∫y0Rdy=y33y220R=23R=mnR⇒m+n=2+3=5

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