Time period of moon is given by: T^2=\\dfrac {4\\pi^2}{GM}r^3 , where M is the mass of the Earth. T=27 daysWhen mass of the Earth is 4M , {T^{'}}^2=\\dfrac {4\\pi^2}{4MG}r^3=\\dfrac {T^2}{4} \\Rightarrow T^{'}=\\dfrac{T}{2}=\\dfrac{27}{2}=14 days