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Work, Energy And Power

Question

Wired Faculty App

A mass M is tied to the top of two identical poles of height H using massless strings of equal length. The mass is at height h above the ground at equilibrium. If the distance between poles is L the tension in each string will be

$\frac{Mg \sqrt{{(\frac{L}{2})}^{2} + {(H - h)}^{2}}}{2 (H - h)}$

$\frac{Mg \sqrt{L^{2} + H^{2}}}{2 (H - h)}$

$\frac{Mg \sqrt{L^{2} + H^{2}}}{2 H}$

$\frac{Mg \sqrt{h^{2} + L^{2}}}{2 L}$

Solution

A.

$\frac{Mg \sqrt{{(\frac{L}{2})}^{2} + {(H - h)}^{2}}}{2 (H - h)}$

At equilibrium

Mg = 2 T sinθ

T = $\frac{M g}{2 sinθ}$ .......(i)

Here, sinθ = $\frac{(H - h)}{\sqrt{{(\frac{L}{2})}^{2} + {(H - h)}^{2}}}$

From equaton (i)

T = $\frac{Mg \sqrt{(\frac{L}{2}) + {(H - h)}^{2}}}{2 (H - h)}$

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