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Q.

A metal wire of length 0.5 m and cross-sectional area $10^{- 4} m^{2}$ has breaking stress $5 \times 10^{8} {Nm}^{- 2}$ . A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be____ ${ms}^{- 1}$

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answer is 50.

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Detailed Solution

$\begin{array}{l} T = \frac{{mv}^{2}}{ℓ} = \frac{10 \times v^{2}}{0 .5} = 20 v^{2} \\ T_{max} = Breaking stress \times Area \\ = 5 \times 10^{8} \times 10^{- 4} = 5 \times 10^{- 4} \\ 20 V^{2} = 5 \times 10^{4} \\ V = \sqrt{\frac{1}{4} 10^{4}} = 50 m / s \end{array}$

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A metal wire of length 0.5 m and cross-sectional area 10−4m2 has breaking stress 5×108 Nm−2. A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be____ ms−1