Question

A simple pendulum of length $L$ and mass $m$ is oscillating in a plane about a vertical line between angular limits $-\varphi$ and $+\varphi$ . For an angular displacement $\theta$ (when |$\theta$| < |$\varphi$| ), the tension in string and the velocity of the bob are T and v respectively. Then the conditions satisfied are

• A. $T=mg\cos \theta$
• B. $T\cos \theta =mg$
• C. $T-mg\cos \theta =\frac{m{v}^2}{L}$
• D. Tangential acceleration is $g\sin \theta$

Answer 1

Answer: (C), (D)

The correct options are
C $T-mg\cos \theta =\frac{m{v}^2}{L}$
D Tangential acceleration is $g\sin \theta$

$equationintangentialdirectionisMgsin\theta =M{a}_{tan}\Rightarrow a_{tan}=gsin\theta equationinradialdirectionisT-Mgcos\theta =\frac{M{v}^2}{r}$