Question

If the speed (v) of the bob in simple pendulum is plotted against the tangential acceleration (a), the correct graph will be represented by

Answer 1

The pendulum bob executes a simple harmonic motion ( position is sinusodial )

Let us assume the position with respect to the equilibrium state to be $n=A\sin (w++Q)$

Thus velocity is given by $v=\frac{dx}{dt}=Aw\cos (w++Q)$

similarly acceleration is given by $a=\frac{dv}{dt}$

$=-A{w}^2\sin (w++Q)$

$\Rightarrow {\left(\frac{a}{A{w}^2}\right)}^2+{\left(\frac{v}{Aw}\right)}^2=1$

Clearly $a-v$ curve is ellipse.

Hence, solved.