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.

Answer 1

(a) smallest at the top and gradually increases down the rod

Explanation: For a hanged heavy uniform rod, at any cross-section, the load is only of the part of the rod which is below it. At its lowest point, the load is zero which gradually increases as we go up. Since the cross-section is the same, the stress increases as we go up. The maximum stress will be at the top and so will be the effect of elongation. Since the transverse strain is proportional to longitudinal strain, hence the diameter of the rod will be smallest at the top and gradually increase down the rod.

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Answer 2

A heave uniform rod is hanging vertically form a fixed support. It is stretched by its won weight.

(a)The diameter of the rod gradually increases down the rod and looks small

Explanation:

• At any cross-section, for a hanged heavy uniform rod, the load that is present below is considered as only a part of the rod.
• The load is zero at its lowest point, which increases gradually as we go up.
• The stress also increases as the cross-section is the same.
• It is to be noted that the maximum stress will be above, so will be the elongation’s effect.
• It is to be noted that the longitudinal strain and the transverse strain are proportional to each other.
• Hence, the rod’s diameter will be small on the top and it increases gradually down the rod.