A) accelerations of both the particles are equal
B) acceleration of the particle of mass \[{{m}_{1}}\]a is proportional to \[{{m}_{1}}\]
C) acceleration of the particle of mass \[{{m}_{1}}\]is proportional to \[{{m}_{2}}\]
D) acceleration of the particle of mass \[{{m}_{1}}\]is inversely\[{{m}_{1}}\] proportional to\[{{m}_{1}}\]
Correct Answer: C
Solution :
The gravitational force acting between the two masses \[{{m}_{1}}\]and \[{{m}_{2}}\]is given by \[{{F}_{G}}=\frac{G{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}\] Force on mass \[{{m}_{1}}\], \[{{F}_{1}}=\frac{G{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}={{m}_{1}}{{a}_{1}}\] where, \[{{a}_{1}}=\]acceleration \[\Rightarrow \] \[{{a}_{1}}=\frac{G{{m}_{2}}}{{{r}^{2}}}\Rightarrow {{a}_{1}}\propto {{m}_{2}}\] and similarly, \[{{a}_{2}}\propto {{m}_{1}}\]
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