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Dimensional Analysis

Question

Consider two cylindrical rods of identical dimensions, one of rubber and the other of steel. Both the rods are fixed rigidly at one end to the roof. A mass $M$ is attached to each of the free ends at the centre of the rods.
Both the rods will elongate but there shall be no perceptible change in shape
The steel rod will elongate and change shape but the rubber rod will only elongate
The steel rod will elongate, without any perceptible change in shape, but the rubber rod will elongate with the shape of the bottom edge tapered to a tip at the centre
The steel rod will elongate without any perceptible change in shape, but the rubber rod will elongate and the shape of the bottom edge will change to an ellipse

A

Both the rods will elongate but there shall be no perceptible change in shape

B

The steel rod will elongate and change shape but the rubber rod will only elongate

C

The steel rod will elongate, without any perceptible change in shape, but the rubber rod will elongate with the shape of the bottom edge tapered to a tip at the centre

D

The steel rod will elongate without any perceptible change in shape, but the rubber rod will elongate and the shape of the bottom edge will change to an ellipse

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Solution

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According to the diagram shown below in which a man $A T$ is attached at the center of each rod, then both rods will be elongated. But due to different elastic properties of the material the steel rod will elongate without making any perceptible change in shape, but the rubber rod will elongate with the shape of the bottom edge tapered to a tip at the centre.

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