Q. What is the velocity of the bob of a simple pendulum at its mean position, if it is able to rise to vertical height of 10 cm? (g=9.8 $ms^{- 2}$ )

A) $2.2\ ms^{- 1}$
B) $1.8\ ms^{- 1}$
C) $1.4\ ms^{- 1}$
D) $0.6\ ms^{- 1}$
Explanation

(c) The bob possess kinetic energy at its mean position which gets converted to potential energy at height$\ \ h$. But the total energy remains converted.
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Hence, we have
KE=PE
Let velocity of the bob at mean position be $v\ and\ m$ be its mass, then we have
$\frac{1}{2}mv^{2} = mgh$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v = \sqrt{2gh}$
Putting g$\ = 9.8\ ms^{- 2},\ h = 0.1\ m$
$\therefore$ $v = \sqrt{2 \times 9.8 \times 0.1} = 1.4\ ms^{- 1}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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