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Question

# If mass of earth decreases by 25% and its radius increases by 50%, then acceleration due to gravity at its surface decreases by nearly:

A
89%
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B
67%
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C
33%
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D
11%
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Solution

## The correct option is B 67%we know thatg=GMR2The mass of the earth decrease by 25% , remaining 75% of M=75100Mradius of earth increase by 50% ,new radius =150% of R=150100Rg′=G(75100M)(150R100)2g′=GMR2[75100×10000150×150]g′=g515g′=0.33gThe acceleration due to gravity decreases by =g−0.33g=0.67gThe acceleration due to gravity decreases by =0.67×100%=67%Hence the acceleration due to gravity at its surface decreases by nearly 67%.

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