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 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 times 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

Since the work done on object is stored as potential energy of object,

$W=mg\Delta h$

$⟹\frac{W_A}{W_B}=\frac{\Delta h_A}{\Delta h_B}=\frac{15}{60}=\frac{1}{4}$

$⟹\Delta h_B=4\Delta h_A$