Two blocks of masses 1 kg and 2 kg are connected by a metal wire going over a smooth pulley as shown in figure. The breaking stress of the metal is $2 imes 10^{9}\ {Nm}^{- 2}$. What should be the minimum radius of the wire used if it is not to break? Take $g = 10\ {ms}^{- 2}$ [image:5_image123.jpeg]

Question

Two blocks of masses 1 kg and 2 kg are connected by a metal wire going over a smooth pulley as shown in figure. The breaking stress of the metal is $2 	imes 10^{9}\ {Nm}^{- 2}$. What should be the minimum radius of the wire used if it is not to break? Take $g = 10\ {ms}^{- 2}$ [image:5_image123.jpeg]

Dr. Abubacker · Accepted Answer

(a) Let the tension in the wire be T . The equations of motion of the two locks are,
$T - 10 = 1\ a$
$and\ \ 20 - T = 2\ a$
Eliminating $a$ form these equations,
$T = \left( \frac{40}{3} ight)N$
$Stress,\ T = \frac{\left( \frac{40}{3} ight)}{\pi\ r^{2}}$
If the minimum radius needed to avoid breakings is $r.$
$2 	imes 10^{9} = \frac{\left( \frac{40}{3} ight)}{\pi\ \ r^{2}}$
Solving this,
$r = 4.6 	imes 10^{- 5}\ m$

Q. Two blocks of masses 1 kg and 2 kg are connected by a metal wire going over a smooth pulley as shown in figure. The breaking stress of the metal is $2 \times 10^{9}\ {Nm}^{- 2}$. What should be the minimum radius of the wire used if it is not to break? Take $g = 10\ {ms}^{- 2}$

Explanation

Reviewed by Dr. Abubacker

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