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Q.

A 5 kg rod of square cross section 5cm on a side and 1m long is pulled along a smooth horizontal surface by a force applied at one end. The rod has a constant acceleration of2m/s2 . Determine the elongation in the rod. (Young’s modulus of the material of the rod is5×109N/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 can’t be determine from the given situation

c

0.4μm

d

16 μm

answer is C.

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Detailed Solution

Let the force applied be p: thenP=ma=5×2=10NFor the element shown in the following figureT=ml(l−x)×a=51(1−x)×2=10(1−x)Elongation in dx is Δ(dx)dx=T/AYΔ(dx)=10(1−x)(5×10−2)2×15×109dxTotal elongationΔl=∫0110(1−x)25×10−4×15×109dx=0.4×10−6m
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