Answer
The mass of the planet is $4.08\times 10^{24}~kg$
Work Step by Step
We can find the free-fall acceleration $g'$ on this planet as:
$y = \frac{1}{2}g't^2$
$g' = \frac{2y}{t^2}$
$g' = \frac{(2)(100~m)}{(6.0~s)^2}$
$g' = 5.56~m/s^2$
We then use the free-fall acceleration to find the mass $M_p$ of the planet.
$\frac{G~M_p}{R^2} = g'$
$M_p = \frac{R^2~g'}{G}$
$M_p = \frac{(7.0\times 10^6~m)^2~(5.56~m/s^2)}{6.67\times 10^{-11}~m^3/kg~s^2}$
$M_p = 4.08\times 10^{24}~kg$
The mass of the planet is $4.08\times 10^{24}~kg$.
