Question

Fifteen joules of work is done on object A so that only its gravitational potential energy changes. Sixty joules of work is done on object B (same mass as object A) so that only its gravitational potential energy changes.
How many times does the height of object B change compared to the height change of object A, as a result of the work done?

• A. Object B changes height four times as much as object A changes height
• B. Object B changes height sixteen times as much as object A changes height.
• C. Object B changes height two times as much as object. A changes height
• D. Object B changes height less than two as much as object A changes height (but not the same amount ).
• E. Object B changes height the same amount as object A changes height.

Answer 1

The correct option is A Object B changes height four times as much as object A changes height

Potential energy of an object at a height is defined by the work done in lifting the object to that height.

Potential energy of a mass $m$ , raised to a height $h$ is given by ,

$U=mgh$ ,where g=gravitational acceleration ,

for object A , work done $=15J=U_A$ ,

or $U_A=mg{h}_A$

or $15=mg{h}_A$ ........................................eq1

similarly for object A , work done $=60J=U_B$ ,

or $U_B=mg{h}_B$

or $60=mg{h}_B$ ....................................eq2

dividing eq2 by eq1 ,

$mg{h}_B/mg{h}_A=60/15$

or $h_B/h_A=4$

or $h_B=4h_A$