Question 114: 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)

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

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)

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