# Chapter 10 - Problems - Page 401: 68

The new period of this pendulum is $2.8~s$

#### Work Step by Step

We can write an expression for the original period of the pendulum: $T = 2\pi~\sqrt{\frac{L}{g}}$ The period does not depend on the mass of the bob, so changing the mass of the bob does not affect the period. We can write an expression for the new period of the pendulum: $T' = 2\pi~\sqrt{\frac{2L}{g}}$ $T' = \sqrt{2}\times 2\pi~\sqrt{\frac{L}{g}}$ $T' = \sqrt{2}\times T$ $T' = (\sqrt{2})(2.0~s)$ $T' = 2.8~s$ The new period of this pendulum is $2.8~s$.

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