In List-I different configurations of uniform rod of mass m, length L, cross-sectional area 'A' and Young's modulus of elasticity 'Y' are as shown. Match the List-I with List-

Question

In List-I different configurations of uniform rod of mass m, length L, cross-sectional area 'A' and Young's modulus of elasticity 'Y' are as shown. Match the List-I with List-II.

List - I	List - II
A rod is hanging vertically with fixed support.	(1) Total elongation in the rod is $\frac{m gL}{2 A Y}$
A constant force $F = m g$ is applied at one end of the rod.	(2) Total elongation in the rod is $\frac{m gL}{A Y}$
Equal and opposite forces ( $F = m g$ ) are applied at both ends of the rod.	(3) Uniform stresses developed in the rod.
A rod is rotating with constant angular velocity about end point in gravity free space.	(4) Non-uniform stress developed in the rod.
	(5) Elastic potential energy stored in the rod is $\frac{m ^{2} g ^{2} L}{6 A Y}$

TestHub · Accepted Answer

P (hanging): tension falls linearly from mg to 0, so elongation $\frac{m gL}{2 A Y}$ , non-uniform stress, energy $\frac{m ^{2} g ^{2} L}{6 A Y}$ → 1,4,5

Q (force mg at one end): same linear tension profile as P → 1,4,5

R (equal opposite forces): uniform tension mg throughout, elongation $\frac{m gL}{A Y}$ , uniform stress → 2,3

S (rotating): tension varies along the rod, net elongation $\frac{m gL}{A Y}$ → 2,4

Answer (A)

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