The string of pendulum of length ' $L$ ' is displaced through $90^{\circ}$ from the vertical and released.…
The string of pendulum of length ' $L$ ' is displaced through $90^{\circ}$ from the vertical and released. Then the maximum strength of the string in order to withstand the tension, as the pendulum passes through the mean position is ( $\mathrm{m}=$ mass of pendulum, $\mathrm{g}=$ acceleration due to gravity)
mg
3 mg
5 mg
6 mg
Solution
By conservation of energy
$\begin{aligned}
& \text { K.E. }=\frac{1}{2} \mathrm{mv}^2=\mathrm{mg} l \\
& \mathrm{v}=\sqrt{2 \mathrm{~g} l}
\end{aligned}$ The forces acting on the pendulum at mean position are tension in string, centripetal force and weight of pendulum.
$\begin{aligned}
& \mathrm{T}-\frac{\mathrm{mv}^2}{l}=\mathrm{mg} \\
& \mathrm{~T}-\frac{\mathrm{m}(\sqrt{2 \mathrm{~g} l})^2}{l}=\mathrm{mg} \\
& \therefore \quad \mathrm{~T}=3 \mathrm{mg}
\end{aligned}$
...[From (i)]