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Standard XII

Physics

Buoyant Force

Two blocks of...

Question

Two blocks of masses $m$ and $2 m$ are connected through a wire of breaking stress $S$ passing over a frictionless pulley. The maximum radius of wire used so that the wire may not break is

\sqrt{\frac{3}{4} \frac{m g}{π S}}

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\sqrt{\frac{4}{3} \frac{m g}{S}}

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\sqrt{\frac{4}{3} \frac{m g}{π S}}

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\sqrt{\frac{1}{2} \frac{m g}{π S}}

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Solution

The correct option is C $\sqrt{\frac{4}{3} \frac{m g}{π S}}$
Stress in the wire $= \frac{T e n s i o n}{A r e a}$
to wire breaking, the stress should not exceed the breaking stress
Let tension be T. Then equations of motions :
$T - m g = m a - 1$
$2 m g - T = 2 m a - 2$
$S o, T = \frac{4 m g}{3}$ from above 2 equation.
$S t r e s s = \frac{4 m g}{3 π r^{2}}$
$S o, S = \frac{4 m g}{3 π r^{2}}$
$r^{2} = \frac{4 m g}{3 π S}$
$o r, r \sqrt{\frac{4 m g}{3 π S}}$

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Two blocks of masses m and 2m are connected through a wire of breaking stress S passing over a frictionless pulley. The maximum radius of wire used so that the wire may not break is

The correct option is C √43mgπSStress in the wire =TensionAreato wire breaking, the stress should not exceed the breaking stressLet tension be T. Then equations of motions :T−mg=ma−12mg−T=2ma−2So,T=4mg3 from above 2 equation.Stress=4mg3πr2So,S=4mg3πr2r2=4mg3πSor,r√4mg3πS

Two blocks of masses $m$ and $2 m$ are connected through a wire of breaking stress $S$ passing over a frictionless pulley. The maximum radius of wire used so that the wire may not break is