Question

A block of weight 10 N is fastened to one end of a wire of cross-sectional area 3 mm² and is rotated in a vertical circle of radius 20 cm. The speed of the block at the bottom of the circle is 2 m s^-1. Find the elongation of the wire when the block is at the bottom of the circle. Young modulus of the material of the wire = 2 x 10¹¹ N m^-2.

• A. ${10}^{-4}$
• B. ${10}^{-3}$
• C. 2 $\times$${10}^{-3}$cm
• D. 2 $\times$${10}^{-4}$cm

Answer 1

The correct option is B

${10}^{-3}$

Forces acting on the block are (a) the tension T and (b) the weight W. At the lowest point, the resultant force is T - W towards the centre. As the block is going in a circle, the net force towards the centre should be mv²/r with usual symbols. Thus,
or, T-W=$\frac{m{v}^2}{r}$
$T=W+\frac{m{v}^2}{r}$
$=10N+\frac{\left(1kg\right)(2m{s}^{-1}{)}^2}{0.2m}=30N$
We have Y=$\frac{\frac{T}{A}}{\frac{l}{L}}$
or, $l=\frac{TL}{AY}$
=$\frac{30N\times \left(20cm\right)}{(3\times {10}^{-6}{m}^2)\times (2\times {10}^{11}N{m}^{-2})}$
$5\times {10}^{-6}\times 20cm={10}^{-3}cm$