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Q.

First an object is slowly lifted from the bottom (point – A) of a thin tunnel of depth h1=R2  to earth’s surface (point - B) and then it is slowly lifted still higher to attain an altitude  h2=R2  above the earth’s surface (Point C).  W1 and W2  are the work performed by external agent in two cases respectively. Consider earth to be a uniform solid sphere and choose the CORRECT option(s)

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a

W1>W2

b

W1

c

W1+W2W1−W2=17

d

W1+W2W1−W2=9

answer is A.

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Detailed Solution

Fex={GMmR3r→ if  0≤r≤RGMmr3r→ if  R≤r<∞​​W1=∫R/2R43πGρmxdx=4πGρm3x22R/2R=3GMm8R   here Mass of the earth=M=​4πR3ρ3W2=∫R3R/2GMmx2dx=GMm x-2+1-2+1R3R2=   GMm3R​⇒W1W2=98   [Hence, W1>W2]⇒|W1+W2W1−W2|=17
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