Question

A simple pendulum of length $l$ is suspended from the ceiling of a cart which is sliding without friction on an inclined plane of inclination $\theta $ . What will be the time period of the pendulum?

• A. $2\pi \sqrt{\frac{l}{g cos \theta }}$
• B. $2\pi \sqrt{\frac{3 l}{g cos \theta }}$
• C. $4\pi \sqrt{\frac{2 l}{g cos \theta }}$
• D. $3\pi \sqrt{\frac{4 l}{2 g cos \theta }}$

Answer 1

Answer: (A)

Here, the point of suspension has an acceleration. $\vec{\text{a}}$ $=gsin\theta $ (down the plane). Further, $\vec{g}$ can be resolved into two components $gsin\theta $ (along the plane) and $gcos\theta $ (perpendicular to the plane).

$\vec{g}_{eff}=\vec{g}-\vec{a}$
$=gcos\theta $ (perpendicular to plane)
$T=2\pi \sqrt{\frac{l}{\left|\right. \vec{g}_{eff} \left|\right.}}$
$=2\pi \sqrt{\frac{l}{g cos \theta }}$