## College Physics (4th Edition)

Published by McGraw-Hill Education

# Chapter 10 - Problems - Page 402: 85

#### Answer

(a) The period of the pendulum on the moon is greater than $T$. (b) $\frac{T_m}{T} = \sqrt{6}$ (c) The period of the mass-spring system on the moon is equal to $T$. (d) $\frac{T_m}{T} = 1$

#### Work Step by Step

(a) We can write the expression for the period of a pendulum: $T = 2\pi~\sqrt{\frac{L}{g}}$ We can see that decreasing $g$ will increase the period. Therefore, the period of the pendulum on the moon is greater than $T$. (b) We can find the ratio $\frac{T_m}{T}$: $T_m = 2\pi~\sqrt{\frac{L}{(g/6)}}$ $T_m = \sqrt{6}\times 2\pi~\sqrt{\frac{L}{g}}$ $T_m = \sqrt{6}~T$ $\frac{T_m}{T} = \sqrt{6}$ (c) We can write the expression for the period of a mass-spring system: $T = 2\pi~\sqrt{\frac{m}{k}}$ We can see that decreasing $g$ will have no effect on the period. Therefore, the period of the mass-spring system on the moon is equal to $T$. (d) Since $T_m = T$, we can see that $\frac{T_m}{T} = 1$

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