question_answer

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? \[(g=9.8\,\,m/{{s}^{2}})\]

A)  2.2 m/s        

B)  1.8 m/s

C)  1.4 m/s        

D)  0.6 m/s

Correct Answer: C

Solution :

Key Idea: 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                 KE = PE Let velocity of bob at mean position to v and m be its mass, then we have                 \[\frac{1}{2}m{{v}^{2}}=mgh\] Putting g = 9.8 \[m/{{s}^{2}}\], h = 0.1 m \[\therefore \] \[v=\sqrt{9.8\times 0.1}=1.4\,m/s\].