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13.Oscillations
hard
The angular amplitude of a simple pendulum is $\theta_0$. The maximum tension in its string will be
A
$mg \left(1-\theta_0\right)$
B
$mg \left(1+\theta_0\right)$
C
$mg \left(1-\theta_0^2\right)$
D
$mg \left(1+\theta_0^2\right)$
(AIIMS-2016)
Solution
(d)
Maximum tension in the string is
$T_{\max }=m g+\frac{m v^2}{l}$
$=m g+\frac{2 m g l}{l}\left(1-\cos \theta_0\right)$
$=m g+2 m g\left(1-1+\frac{\theta_0^2}{2}\right) \text { (since } \theta_0 \text { is small) }$
$=m g\left(1+\theta_0^2\right)$
Standard 11
Physics
