A) At 2.05 m from 10 kg mass
B) At 2.05 m from 20 kg mass
C) At 2.95 m from 10 kg mass
D) At 3 m from 20 kg mass
Correct Answer: A
Solution :
Force on 30 kg mass due to 10 kg mass. \[{{F}_{1}}=6.67\times {{10}^{-11}}\times \frac{10\times 30}{{{x}^{2}}}\] towards left Force on 30 kg mass due to 20 kg mass \[{{F}_{2}}=6.67\times {{10}^{-11}}\times \frac{30\times 20}{{{(5-x)}^{2}}}\]towards right Since the net force of 30 kg mass is zero, \[\therefore \] \[{{\text{F}}_{\text{1}}}\text{=}{{\text{F}}_{\text{2}}}\] \[\therefore 6.67\times {{10}^{-11}}\times \frac{10\times 30}{{{x}^{2}}}\] \[=6.67\times {{10}^{-11}}\times \frac{30\times 20}{{{(5-x)}^{2}}}\] Or \[{{(5-x)}^{2}}=2{{x}^{2}}\] or \[25+{{x}^{2}}-10x=2{{x}^{2}}\] Or \[{{x}^{2}}+10x-25=0\] \[x=2.05m\]You need to login to perform this action.
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