Question

An astronaut drops a marble on the surface of Mars and observes that it takes 1.02 s for the marble to fall 2.00 m. She also knows that the radius of Mars is 3.39 × 106 m and that G = 6.67 x 10-11 N·m2/kg2. From this information, she can conclude that the mass of Mars is

Answer 1

Answer:

The mass of mars is $6.61\times10^{23}\ kg$

Explanation:

Given that,

Time = 1.02 s

Height = 2.00 m

Radius of mars $r= 3.39\times10^{6}\ m$

We need to calculate the acceleration due to gravity on mars

Using equation of motion

$h = ut+\dfrac{1}{2}gt^2$

$h = \dfrac{1}{2}gt^2$

$g=\dfrac{2h}{t^2}$

Where, u = initial velocity

t = time

h = height

Put the value into the formula

$g=\dfrac{2\times2.00}{(1.02)^2}$

$g=3.84\ m/s^2$

We need to calculate the mass of mars

Using formula of gravity

$g=\dfrac{Gm}{r^2}$

Put the value into the formula

$3.84=\dfrac{6.67\times10^{-11}\times m}{(3.39\times10^{6})^2}$

$m=\dfrac{3.84\times(3.39\times10^{6})^2}{6.67\times10^{-11}}$

$m=6.61\times10^{23}\ kg$

Hence, The mass of mars is $6.61\times10^{23}\ kg$