Answer:
Approximately [tex]13\; {\rm kg}[/tex], assuming that [tex]g = 9.81\; {\rm N \cdot kg^{-1}}[/tex].
Explanation:
The gravitational field is approximately uniform ([tex]g \approx 9.81\; {\rm N\cdot kg^{-1}}[/tex]) near the surface of the Earth.
Consider an object of mass [tex]m[/tex] in this gravitational field. If the height of this object increases by [tex]\Delta h[/tex], this object would gain gravitational potential energy ([tex]\text{GPE}[/tex]) [tex]m\, g\, \Delta h[/tex].
In this question, it is given that [tex]\Delta h = 1.5\; {\rm m}[/tex]. The object gained [tex]187.5\; {\rm J}[/tex] of [tex]\text{GPE}[/tex]. Rearrange the equation [tex]\text{GPE} = m\, g\, \Delta h[/tex] to find the mass of this object:
[tex]\begin{aligned}m &= \frac{(\text{GPE})}{g\, \Delta h} \\ &= \frac{187.5\; {\rm J}}{(9.81\; {\rm N\cdot kg^{-1}})\, (1.5\; {\rm m})} \\ &\approx 13\; {\rm kg} \end{aligned}[/tex].
(Note that [tex]187.5\; {\rm J} = 187.5\; {\rm N\cdot m}[/tex].)
