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