Work Done By Gravity On A Projectile

Question

A ball is thrown vertically upward and returns to the same height from which it was launched on a windless day. What is the total work done by gravity over the complete up-and-down journey of the ball?

RankGuru · Accepted Answer

As explained in NCERT Class 11, Chapter 6 (Work, Energy and Power), gravity is a conservative force, and the work it does depends only on the change in vertical position between the start and end points. Since the ball returns to its starting height, the net vertical displacement is zero, so the total work done by gravity over the whole trip is zero. On the way up gravity does negative work equal to mgh, and on the way down it does an equal positive work of mgh, and these cancel exactly. The option about twice the maximum potential energy confuses magnitudes with net work. The option about maximum kinetic energy mislabels the result. The option giving negative mgh accounts for only the upward half. A consistency check: for any conservative force, a closed path or a return to the same height yields zero net work, confirming the answer is zero.

Work Done By Gravity On A Projectile

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