A small coherent asteroid with a density of 2,300 kgm3 is hit with a large metal projectile from a spacecraft experiment

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A small coherent asteroid with a density of 2,300
kgm3 is hit with a large metal projectile from a
spacecraft experiment and breaks up completely. The sizes of the
pieces follow the approximate power-law size distribution:
N(R) = C(R/1.00
m)-3 dR
where C = 100 m-1 and 1.00 mm
≤ R ≤ 1.00 m.
Determine the total mass of the asteroid by integrating over the
size distribution. Hint: Determine dm the total mass
of number of particles N(R) of radius
exactly R (actually within the radius interval
[R, R + dR])
(Answer in kg and in scientific notation using 2 sig. figs.)