First slide

Elastic behaviour of solids

Question

A body of mass $m = 10 k g$ is attached to one end of a wire of length 0.3 m. The maximum angular speed (in rad $s^{- 1}$ ) with which it can be rotated about its other end in space station is (Breaking stress of wire $= 4.8 \times 10^{7} N m^{- 2}$ and area of cross section of the wire $= 10^{- 2} c m^{2}$ ) is :

Easy

Solution

$C e n t r i p e t a l f o r c e i s p r o v i d e d b y t e n s i o n i n s t r i n g .$
$∴ m l ω^{2} = T$
$\Rightarrow m l ω^{2} = σ A h e r e σ = b r e a k i n g s t r e s s$
$\Rightarrow ω = \sqrt{\frac{σ A}{m l}} = \sqrt{\frac{(4.8 \times 10^{7}) 10^{- 6}}{10 \times 0.3}} = 4 r a d / \sec$

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