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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 sress of the metal is 2×109N m2. What should be the minimum radius of the wire used if it is not to break? Take g=10m s2.

A
3.8×106m
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B
4.6×105m
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C
3.4×108m
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D
2.4×104m
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Solution

The correct option is B 4.6×105m
The stress in the wire = TensionArea of cross section.
To avoid breaking, this stress should not exceed the breaking stress.
Let the tension in the wire be T. The equations of motion of the two blocks are,
and T = 10 N = (1 kg) a
20 N - T = (2 kg) a.
Eliminating a from these equations,
T = (40/3) N.
(40/3) N
The stress = πr2

If the minimum radius needed to avoid breaking is r,
2×109Nm2=(40/3)Nπr2

Solving this,
r = 4.6 × 105 m.

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