A uniform rope of length - lies on a table- If the co -1 of the part of this rope which can overhang from the edge of the table without sliding down is-

The correct option is C ul1+ μ weight of over hanging part =mgl_1g weight of rope lying on the table =ml(l l_1)g normal reaction R=ml(l l_1)g , ...

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Standard X

Chemistry

Factors Affecting the Rate of a Chemical Reaction

A uniform rop...

Question

A uniform rope of length $ℓ$ lies on a table. If the co $ℓ_{1}$ of the part of this rope which can overhang from the edge of the table without sliding down is:

\frac{l}{μ}

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\frac{l}{μ + 1}

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\frac{u l}{1 + μ}

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\frac{μ l}{1 - μ}

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Solution

The correct option is C $\frac{u l}{1 + μ}$
weight of over hanging part $= \frac{m}{g} l_{1} g$
weight of rope lying on the table $= \frac{m}{l} (l - l_{1}) g$
normal reaction $R = \frac{m}{l} (l - l_{1}) g, F = μ R ⟹ F = μ \frac{m}{l} (l - l_{1}) g$
the rope will not slide down when $\frac{m l_{1} g}{l} < F$
$\frac{m l_{1} g}{l} < μ \frac{m}{l} (l - l_{1}) g ⟹ l_{1} < μ (l - l_{1})$
for maximum value of $l_{1} ⟹ l_{1} = μ (l - l_{1}) ⟹ l_{1} = \frac{μ l}{1 + μ}$

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A uniform rope of length ℓ lies on a table. If the co ℓ1 of the part of this rope which can overhang from the edge of the table without sliding down is:

The correct option is C ul1+μweight of over hanging part=mgl1gweight of rope lying on the table=ml(l−l1)gnormal reactionR=ml(l−l1)g ,F=μR⟹F=μml(l−l1)gthe rope will not slide down when ml1gl<Fml1gl<μml(l−l1)g⟹l1<μ(l−l1)for maximum value ofl1⟹l1=μ(l−l1)⟹l1=μl1+μ

A uniform rope of length $ℓ$ lies on a table. If the co $ℓ_{1}$ of the part of this rope which can overhang from the edge of the table without sliding down is: