Question

The mass of the bob of a simple pendulum of length $L$is $m$. If the bob is left from its horizontal position then the speed of the bob and the tension in the thread in the lowest position of the bob will be respectively.

• A. $\sqrt{2gL}$and$3mg$
• B. $3mg$ and $\sqrt{2gL}$
• C. $2mg$and$\sqrt{2gl}$
• D. $2gl$ and $3mg$

Answer 1

Answer: (A)

$\sqrt{2gL}$and$3mg$

Answer 2

By the conservation of energy

Potential energy at point A = Kinetic energy at point B

$mgl = \frac{1}{2}mv^{2}$ $\Rightarrow v = \sqrt{2gl}$

and tension$= mg + \frac{mv^{2}}{l} \Rightarrow T = mg + \frac{m}{l}(2gl) \Rightarrow T = 3mg$