The trolley car having simple pendulum decelerated by friction. In consequence, the pendulum has time period T…

Q: The trolley car having simple pendulum decelerated by friction. In consequence, the pendulum has time period T. If T0 is time period of the simple pendulum in the absence of any acceleration of the trolley car, the value of T/T0 is …

Sol: $\large T = 2\pi \sqrt{\frac{l}{\sqrt{g^2 + a^2}}}$

a = μ g

$\large T = 2\pi \sqrt{\frac{l}{g \sqrt{1 + \mu^2}}}$

$\large T = T_0 \sqrt{\frac{1}{\sqrt{1 + \mu^2}}}$

$\large \frac{T}{T_0} = \sqrt{\frac{1}{\sqrt{1 + \mu^2}}}$