Answer
The period on Mars is 2.60 seconds.
Work Step by Step
(a) We can find the length of the pendulum.
$T = 2\pi~\sqrt{\frac{L}{g}}$
$L = \frac{T^2~g}{(2\pi)^2}$
$L = \frac{(1.60~s)^2(9.80~m/s^2)}{(2\pi)^2}$
$L = 0.6355~m$
We can find the period on Mars.
$T_M = 2\pi~\sqrt{\frac{L}{g_M}}$
$T_M = 2\pi~\sqrt{\frac{0.6355~m}{3.71~m/s^2}}$
$T_M = 2.60~s$
The period on Mars is 2.60 seconds.
