Question
Tue December 05, 2017 By: Apurwa Minj

A body of mass m rises to height h=R/5 from the earth's surface, where R is earth's radius. If g is acceleration due to gravity at earth's surface, the increase in potential energy is
(a)mg/h                (b)mgh 5/6
(c)3/5 mgh            (d)6/7 mgh
Answer is : (b)mgh 5/6
 

Expert Reply
Gajendra
Thu December 07, 2017
height on ground=h=R
Increase in h= R/5  h=5R
 
I n c r e a s e space i n space p o t e n t i a l space e n e r g y
equals P E space a t space h space minus space space P E space a t space g r o u n d space s u r f a c e
equals negative fraction numerator G M m over denominator R plus begin display style R over 5 end style end fraction minus open parentheses negative fraction numerator G M m over denominator R end fraction close parentheses
equals negative fraction numerator 5 G M m over denominator 6 R end fraction plus fraction numerator G M m over denominator R end fraction
equals fraction numerator G M m over denominator 6 R end fraction

equals fraction numerator G M m x R over denominator 6 R X R end fraction space equals fraction numerator G M m x space 5 h over denominator 6 R squared end fraction


equals fraction numerator 5 m g h over denominator 6 end fraction
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