Given, four masses are kept at corner of square and side of squares be
a,
As we know that, gravitational force,
F=‌ where,
G is gravitational constant and
d is the separation between two bodies.
If we calculate net force on 2 , then
Since,
F21=F23= force on 2 due to 1 and 3 will be equal.
∴‌F21=F23=‌ ‌ and ‌‌‌F24=‌=‌ Now, as forces are vector quantity and angle between
F21 and
F23 is
90∘.
∴‌‌F‌net ‌‌‌=F24+√F212+F232 ‌‌=‌+√(‌)2+(‌)2 ‌‌=‌+√2(‌)2 ‌‌=‌+‌√2 ‌‌=‌(‌+√2) ‌‌=‌(‌) According to the question,
F‌net ‌=(‌)‌ Therefore,
a2=16L2 a=4L