We present a detailed analysis of HARPS-N radial velocity observations of K2-100, a young and active star in the Praesepe cluster, which hosts a transiting planet with a period of 1.7 days. We model the activity-induced radial velocity variations of the host star with a multi-dimensional Gaussian Process framework and detect a planetary signal of $10.6 pm 3.0 {rm m,s^{-1}}$, which matches the transit ephemeris, and translates to a planet mass of $21.8 pm 6.2 M_oplus$. We perform a suite of validation tests to confirm that our detected signal is genuine. This is the first mass measurement for a transiting planet in a young open cluster. The relatively low density of the planet, $2.04^{+0.66}_{-0.61} {rm g,cm^{-3}}$, implies that K2-100b retains a significant volatile envelope. We estimate that the planet is losing its atmosphere at a rate of $10^{11}-10^{12},{rm g,s^{-1}}$ due to the high level of radiation it receives from its host star.
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