Consider two solid sphers of radii R_1=1m,\: R_2=2m and masses M1 and M2, respectively. The gravitational field due to sphere  and  are shown. The value of \frac{M_1}{M_2} is:  
Option: 1 \frac{2}{3}

Option: 2 \frac{1}{6}

Option: 3 \frac{1}{2}

Option: 4 \frac{1}{3}
 

Answers (1)

Considering Case 2 and case 1, one by one

and using I=\frac{GM}{R^2} \ \ \ \ (\text{Gravitational field on surface of sphere})

R-Radius of sphere

                                                            \\ 3=\frac{\mathrm{Gm}_{2}}{2^{2}} \\ \\ 2=\frac{\mathrm{Gm}_{1}}{1^{2}} \\ \\ \therefore \frac{3}{2}=\frac{1}{4} \frac{\mathrm{m}_{2}}{\mathrm{m}_{1}} \\ \\ \frac{\mathrm{m}_{1}}{\mathrm{m}_{2}}=\frac{1}{6}

So the correct option is 2.

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