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ISRO Scientist ME 2012 Paper

- \(\frac{{mgL}}{{\left( {2\sqrt {{L^3} - {r^2}} } \right)}}\)
- \(\frac{{mgL}}{{\sqrt {{L^2}} }}\)
- \(mgL\sqrt {{r^2}} \)
- \(\frac{{mgL}}{{\sqrt {{L^2} - {r^2}} }}\)

Option 4 : \(\frac{{mgL}}{{\sqrt {{L^2} - {r^2}} }}\)

Free

ST 1: Building Materials

1159

20 Questions
20 Marks
20 Mins

**Concept:**

The FBD of a mass and string is shown in the figure.

At a moment, tension in the string is,

∑f_{y} = 0

T sin θ = mg -----(1)

As, \({sin ~\theta = \frac{{\sqrt {{L^2} - {r^2}} }}{L}}\)

equation 1 becomes

\(T \times \frac{{\sqrt {{L^2} - {r^2}} }}{L} = mg\)

\(T = \frac{{mgL}}{{\sqrt {{L^2} - {r^2}} }}\)

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