Question

What is the velocity of the bob of pendulum at its mean position, if it is a1 to vertical height of $10\, cm$ ? $ (g=9.8\,m/s^{2}) $

• A. 2.2 m/s
• B. 1.8 m/s
• C. 1.4 m/s
• D. 0.6 m/s

Answer 1

Answer: (C)

Total energy remains conserved in simple harmonic motion.
The bob possess kinetic energy at its mean position which gets converted to potential energy at height $h$. But the total energy remains conserved.
Hence, we have
$K E=P E$
Let velocity of bob at mean position to $v$ and $m$ be its mass, then we have
$\frac{1}{2} m v^{2}=m g h$
$\Rightarrow v=\sqrt{2 g h}$
Putting $g=9.8\, m / s ^{2}, h=0.1\, m$
$\therefore v=\sqrt{2 \times 9.8 \times 0.1}=1.4\, m / s$