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Q.

A 5-kg rod of square cross section 5 cm on a side and 1 m long is pulled along a smooth horizontal surface by a force applied at one end. The rod has a constant acceleration of 2ms−2. Determine the elongation in the rod. (Young's modulus of the material of the rod is 5×109N/m2).

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a

Zero, as for elongation to be there, equal and opposite forces must act on the rod

b

Non-zero but cannot be determine from the given situation

c

0.4 μm

d

16 μm

answer is C.

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Detailed Solution

Let the force applied be p, then P = ma⇒ p=5×2=10NFor the element shown in the figure, T=ml(l−x)×a⇒ ⇒T=51(1−x)×2=10(1−x)Elongation in dx is Δ(dx)dx=T/AYΔ(dx)=10(1−x)5×10−22×15×109dxTotal elongation, Δl=∫01 10(1−x)25×10−4×15×109dx=0.4×10−6m

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