Question

# Three uniform spheres are fixed at positions shown Figure. (m_1=3.0 kg, m_2=4.0 kg. and =0.60m.)FSP02510401021.gifFSZ

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Three uniform spheres are fixed at positions shown Figure. ($$\displaystyle{m}_{{1}}={3.0}$$ kg, $$\displaystyle{m}_{{2}}={4.0}$$ kg. and =0.60m.)

2020-11-11
(a) Let m be the mass of the particle at P. Force on 0.055 kg mass =
$$\displaystyle{F}={\left({G}_{{m}}{\frac{{{m}_{{1}}}}{{{d}_{{2}}}}}\right)}{\left({i}+{j}\right)}+{\left({G}_{{m}}{\frac{{{m}_{{2}}}}{{{2}{d}_{{2}}}}}\right)}{\left({i}+{j}\right)}$$
$$\displaystyle={\left({\frac{{{G}_{{m}}}}{{{d}_{{2}}}}}\right)}{\left({m}_{{1}}+{\frac{{{m}_{{2}}}}{{{2}}}}\right)}{\left({i}+{j}\right)}$$
$$\displaystyle={\left({6.673}\times{10}-{11}\times{\frac{{{0.055}}}{{{0.62}}}}\right)}{\left({3.0}+{2.0}\right)}{\left({i}+{j}\right)}$$
$$\displaystyle={5.097}\times{10}^{{-{11}}}{\left({i}+{j}\right)}{N}$$
$$\displaystyle={3.604}\times{10}^{{-{11}}}{N}$$
$$\displaystyle={45}$$
anticlockwise from thex-axis.