Answer:
At 11.5 m
Explanation:
The power per unit area corresponds to the intensity, which is given by
[tex]I=\frac{P}{4\pi r^2}[/tex]
where
P is the power
[tex]4\pi r^2[/tex] is the area irradiated at a distance r from the source (it corresponds to the surface area of a sphere of radius r)
Here we want the intensity of the two light bulbs to be the same, so
[tex]I_1 = I_2\\\frac{P_1}{4 \pi r_1^2}=\frac{P_2}{4\pi r_2^2}[/tex]
where we have
P1 = 100 W is the power of the first light bulb
P2 = 75 W is the power of the second light bulb
r2 = 10 m is the distance from the second light bulb
Solving for r1, we find
[tex]r_1 = r_2 \sqrt{\frac{P_1}{P_2}}= (10 m) \sqrt{\frac{100 W}{75 W}} = 11.5 m[/tex]
