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Standard XII

Physics

Applying NLM along 3 Axis

Two light ver...

Question

Two light vertical springs with spring constants $k_{1}$ and $k_{2}$ are separated by a distance $l$ . Their upper ends are fixed to the ceiling and their lower ends to the ends $A$ and $B$ of a light horizontal rod $A B$ . A vertical downward force $F$ is applied at the point C on the rod, $A B$ will remain horizontal in equilibrium if the distance $A C$ is :

\frac{l k_{1}}{k_{2}}

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\frac{l k_{1}}{k_{2} + k_{1}}

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\frac{l k_{2}}{k_{1}}

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\frac{l k_{2}}{k_{1} + k_{2}}

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Solution

The correct option is D $\frac{l k_{2}}{k_{1} + k_{2}}$
$\sum (Moments about C) = 0$
$∴ (k_{1} x) A C = (k_{2} x) B C$
$∴ \frac{A C}{B C} = \frac{k_{2}}{k_{1}}$
$A C + B C = l$
$Solving these two equations, we get$
$A C = (\frac{k_{2}}{k_{1} + k_{2}}) l$

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The correct option is D lk2k1+k2∑(Moments about C)=0∴(k1x)AC=(k2x)BC∴ACBC=k2k1AC+BC=lSolving these two equations, we getAC=(k2k1+k2)l

The correct option is D $\frac{l k_{2}}{k_{1} + k_{2}}$
$\sum (Moments about C) = 0$
$∴ (k_{1} x) A C = (k_{2} x) B C$
$∴ \frac{A C}{B C} = \frac{k_{2}}{k_{1}}$
$A C + B C = l$
$Solving these two equations, we get$
$A C = (\frac{k_{2}}{k_{1} + k_{2}}) l$