Question

A simple pendulum of length $50cm$ is suspended from a fixed point $O$ and a nail is fixed at a point $P$ which is vertically below $O$ at some distance. The bob is released when string is horizontal. The bob reaches lowest position then it describes vertical circle whose centre coincides with point $P$. The minimum distance between $O$ and $P$ is:

• A. 20 cm
• B. 25 cm
• C. 30 cm
• D. 40 cm

Answer 1

Answer: (C)

30 cm

When the ball just reaches the bottom, from conservation of energy, $v^2=2gL$

But when it reaches the bottom, it describes a vertical circle. hence $v^2=5gr$

where $r$ is the radius of the circle.

Hence $\frac{r}{L}=\frac{2}{5}$

$⟹r=20cm$

Hence minimum distance between O and P=$50cm-20cm=30cm$