A stone of mass 2 kg is fastened to one end of a steel wire of cross sectional area $2 m m^{2}$ and is whirled in a horizontal circle of radius 25cm. If the breaking stress of steel is $1.2 \times 10^{9} N m^{- 2}$ find the maximum number of revolutions the stone can make per minute without the string breaking.

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331.5 rpm

661.5 rpm

441.5 rpm

221.5 rpm

answer is A.

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Detailed Solution

Stress $= \frac{T}{A} \Rightarrow T = s t r e s s \times A$

$T = 1.2 \times 10^{9} \times 2 \times 10^{- 6} = 2.4 \times 10^{3} N$

$T = m r ω^{2} \Rightarrow ω = \sqrt{\frac{T}{m r}} = \sqrt{\frac{2.4 \times 10^{3}}{2 \times 25 \times 10^{- 2}}} = 69.2 r a d / s = 69.2 \times \frac{60}{2 π} = 661.5 r p m$ $(∵ 1 r p m = \frac{2 π}{60} r a d / s)$

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