Answer
The magnitude of the net gravitational force on sphere B is $~~2.13\times 10^{-8}~N$
Work Step by Step
We can find the y-component of the gravitational force on B:
$F_y = \frac{G~m_A~m_B}{d_1^2}$
$F_y = \frac{(6.67\times 10^{-11}~N~m^2/kg^2)(5.00~kg)(5.00~kg)}{(0.300~m)^2}$
$F_y = 1.853\times 10^{-8}~N$
We can find the x-component of the gravitational force on B:
$F_x = \frac{G~m_C~m_B}{d_2^2}$
$F_x = \frac{(6.67\times 10^{-11}~N~m^2/kg^2)(5.00~kg)(5.00~kg)}{(0.400~m)^2}$
$F_x = 1.042\times 10^{-8}~N$
We can find the magnitude of the net gravitational force on sphere B:
$F = \sqrt{F_x^2+F_y^2}$
$F = \sqrt{(1.042\times 10^{-8}~N)^2+(1.853\times 10^{-8}~N)^2}$
$F = 2.13\times 10^{-8}~N$
The magnitude of the net gravitational force on sphere B is $~~2.13\times 10^{-8}~N$