Q83 / 90 · JEE Main 2022 (28 Jul Shift 2) · Physics

A string of area of cross-section 4 mm2 and length 0.5 is connected with a rigid body of mass 2 kg. The body is rotated in a vertical circular path of radius 0.5 m. The body acquires a speed of 5 m s-1 at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is _____ ×10-5. (Use Young's modulus 1011 N m-2 and g=10 m s-2)

Correct answer: 30

Solution

Given here, A=4 mm2, l=0.5 m, m=2 kg and vb=5 m s-1.

Tension at the bottom of the circular motion is given by T=mg+mvb2R

Figure

Using Young's modulus, we have 

Strain produced in the string when the body is at the bottom of the circle is ∆ll=TAY

=mg+mvb2lAY =20+2520.53×10-6×1011=30×10-5

Hence, the correct answer is 30.

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