Question

Review1 Constants Astronauts on the first trip to Mars take along a pendulum that has a period on earth of 1.50 S. The period on Mars turns out to be 2.45 S. Part A What is the Martian free-fall acceleration? Express your answer to three significant figures and include the appropriate units. gMar.- ו Value Units Submit Request Answer Provide Feedback Next >

Answer 1

Time period of the pendulum on the Earth is $T_E=1.50\,s$

Time period of the pendulum on the Mars is $T_M=2.45\,s$

Time period of a pendulum of length $l$ on Earth is $T_E=2\pi\sqrt{\frac{l}{g}}$

Time period of a pendulum of length $l$ on Mars is $T_M=2\pi\sqrt{\frac{l}{g_{mars}}}$ ​​​​​​​

$\frac{T_E}{T_M}=\frac{2\pi\sqrt{\frac{l}{g}}}{2\pi\sqrt{\frac{l}{g_{mars}}}}$

$\frac{T_E}{T_M}=\sqrt{\frac{g_{mars}}{g}}$

$g_{mars}=g\left ( \frac{T_E}{T_M} \right )^2$

$g_{mars}=9.81\left ( \frac{1.5}{2.45} \right )^2=3.68\,m/s^2$