Question 130: Properties of Matter

Question

Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is ${{24} \over \pi } 	imes {10^2}$ Nm
-2
. What is the minimum radius of the wire ? (Take g = 10 ms
-2
)
![](https://imagex.cdn.examgoal.net/1ktemelku/1eea32a7-25c7-43d8-a54f-89ece57d5e18/b23c5de0-125a-11ec-a4fb-5347f21481c0/file-1ktemelkv.jpeg)

Accepted Answer

$T = {{2{m_1}{m_2}g} \over {{m_1} + {m_2}}} = {{2 	imes 3 	imes 5 	imes 10} \over 8}$
$ = {{75} \over 2}$
Stress $ = {T \over A}$
${{24} \over \pi } 	imes {10^2} = {{75} \over {2 	imes \pi {R^2}}}$
${R^2} = {{75} \over {2 	imes 24 	imes 100}} = {3 \over {8 	imes 24}}$
$\Rightarrow$ R = 0.125 m
R = 12.5 cm
![](https://imagex.cdn.examgoal.net/1ktjf0fhf/d63eb9ea-ad5f-46cf-92cf-cce4c2b3e9e5/b38aeb30-14fd-11ec-87b0-2f866bb7de71/file-1ktjf0fhg.jpeg)

Answer

125 cm

Answer

1250 cm

Answer

12.5 cm

Answer

1.25 cm

Properties of Matter

Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is {{24} \over \pi } \times {10^2} Nm -2 . What is the minimum radius of the wire ? (Take g = 10 ms -2 )

Choose the correct answer: