1
Question
A heave uniform rod is hanging vertically form a fixed support. It is stretched by its won weight. The diameter of the rod is
(a) smallest at the top and gradually increases down the rod
(b) largest at the top and gradually decreased down the rod
(c) uniform everywhere
(d) maximum in the middle.
(a) smallest at the top and gradually increases down the rod
(b) largest at the top and gradually decreased down the rod
(c) uniform everywhere
(d) maximum in the middle.
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Solution
Correct option: (a) s​mallest at the top and gradually increases down the rod
As the rod is of uniform mass distribution and stretched by its own weight, the topmost part of the rod experiences maximum stress due to the weight of the entire rod. This stress leads to lateral strain and the rod becomes thinner. Moving down along the length of the rod, the stress decreases because the lower parts bear lesser weight of the rod. With reduced stress, the lateral strain also reduces. Hence, the diameter of the rod gradually increases from top to bottom.
As the rod is of uniform mass distribution and stretched by its own weight, the topmost part of the rod experiences maximum stress due to the weight of the entire rod. This stress leads to lateral strain and the rod becomes thinner. Moving down along the length of the rod, the stress decreases because the lower parts bear lesser weight of the rod. With reduced stress, the lateral strain also reduces. Hence, the diameter of the rod gradually increases from top to bottom.
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