First slide

Conservation of mechanical energy

Question

A simple pendulum of length l and bob of mass m is displaced from its equilibrium position O to a position P so that height of P above O is h. It is then released. What is the tension in the string when the bob passes through the equilibrium position O? Neglect friction. V is the velocity of the bob at O

Moderate

A

$m (g + \frac{v^{2}}{l})$
B

1 and 4 both are correct.
C

$m g (1 + \frac{h}{l})$
D

$m g (1 + \frac{2 h}{l})$

Solution

$\begin{matrix} f r o m e q u a t i o n o f m o t i o n v^{2} = 2 g h \\ f o r v e r t i c a l c i r c u l a r m o t i o n, T - m g = \frac{m v^{2}}{l}, h e r e T i s t e n s i o n i n t h e s t r i n g, m i s m a s s o f b o d y, g \\ g i s a c c e l e r a t i o n d u e t o g r a v i t y, v i s v e l o c i t y o f t h e b o d y, l i s l e n g t h o f t h e s t r i n g \\ \Rightarrow T = m g + \frac{m (2 g h)}{l} \\ \Rightarrow T = m g (1 + \frac{2 h}{l}) \end{matrix}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App