TS EAMCET 4-Aug-2021 Shift 2 Question Paper

Given, four masses are kept at corner of square and side of squares be a,As we know that, gravitational force, F=‌

GM2

d2

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=‌

GM2

a2

‌ and ‌‌‌F24=‌

GM2

(a√2)2

=‌

GM2

2a2

Now, as forces are vector quantity and angle between F21 and F23 is 90∘.
∴‌‌F‌net ‌‌‌=F24+√F212+F232
‌‌=‌

GM2

2a2

+√(‌

GM2

a2

)2+(‌

GM2

a2

)2
‌‌=‌

GM2

2a2

+√2(‌

GM2

a2

)2
‌‌=‌

GM2

2a2

+‌

GM2

a2

√2
‌‌=‌

GM2

a2

(‌

1

2

+√2)
‌‌=‌

GM2

a2

(‌

1+2√2

2

)
According to the question, F‌net ‌=(‌

2√2+1

32

)‌

GM2

L2

Therefore, a2=16L2
a=4L