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Limiting Friction

Two wires of ...

Question

Two wires of the same material but radii $r_{1}$ and $r_{2}$ support a mass M in between. If a force of $F = \frac{1}{3} M g$ is applied then :

for

r_{1} = r_{2}

, 2 should break before 1

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for

r_{1}

less than

2 r_{2}

, 2 should break before 1

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data is insufficient

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for

r_{1} = 2 r_{2}

, any of the two may break

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Solution

The correct option is D for $r_{1} = 2 r_{2}$ , any of the two may break
Wire(2) expriences force $F_{2} = \frac{M_{g}}{3}$
Wire(1) expriences force $F_{1} = \frac{M_{g}}{3} +$ some extension force.
let us consider the options:
(a) $r_{1} = r_{2} \Rightarrow 2$ won't break before $1$ .
(b) for $r_{1} < 2 r_{2} \Rightarrow 2$ won't break before $1$ .
(c) not applicable
(d) $r_{1} = 2 r_{2} \Rightarrow$ resulting force change and thus any of the two can break.
thus ans is (d).

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Two wires of the same material but radii r1 and r2 support a mass M in between. If a force of F=13Mg is applied then :

Two wires of the same material but radii $r_{1}$ and $r_{2}$ support a mass M in between. If a force of $F = \frac{1}{3} M g$ is applied then :