Question

Two, weights of 5kg and 10kg are placed on a horizontal table of height 1.5 m. Which weight will have more potential energy?
(A). 5 kg
(B). 10 kg
(C). Both will have equal energy
(D). None of the above

Answer 1

Hint: The potential energy of a mass m at a height h from ground is mgh, where g is acceleration due to gravity. Since both of them are at the same height, the one with greater mass will have more potential energy.

Complete Step By Step Solution:

Potential energy of a body is negative of work done by conservative force. Here gravity is the conservative force, so we are talking about gravitational potential energy.
Let us calculate gravitational potential energy of a body of a mass m at a height h from ground.
Work done by gravity in moving a body from ground to height h,
Since gravity is almost constant force with its magnitude equal to mg, its work can be written as
$F\cdot s=Fs\cos \theta $ , where $\theta $angle between force and displacement and s is is displacement. Here $\theta $ is 180 degree and s=h, so work of gravity is
${{W}_{g}}=-mgh$
Therefore gravitational potential energy becomes
${{U}_{g}}=mgh$
Gravitational potential energy of 5 kg body on a horizontal table of height 1.5 m is $5\times g\times 1.5=7.5g$ and Gravitational potential energy of 10 kg body on a horizontal table of height 1.5 m is $10\times g\times 1.5=15g$
So the correct option is B.

Note: Here it is assumed that gravitational potential energy at ground is assumed to be zero. If gravitational potential energy, at height same as where objects are kept is assumed to be zero, then gravitational potential energy of both would have been same and correct option would be C. Also if gravitational potential energy, at height above from where objects are kept is assumed to be zero, then gravitational potential energy of 5 kg body would have been more than that of 10 kg body and correct option would be A. But when this reference is not specified we assume it to be at ground. Therefore answer is option B.