Three point masses each of 1kg are placed at three corners of a square of side 2cm the gravitational field at the fourth corner of the square is (approximately)
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a
3.2×10−7N/kg
b
Zero
c
500N/kg
d
4×10−7N/kg
answer is A.
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Detailed Solution
The directions of the individual gravitational fields are as shown in the fig.Gravitational fields due to individual masses Gravitational field strength=Gmr2; universal gravitation constant=G; mass=m; distance=r; due to mass at A: E1=G×12×10−22=1.67×10−7N/kg due to mass at C: E2=G×12×10−22=1.67×10−7N/kg due to mass at B: E3=G×122×10−22=0.834×10−7N/kgThe resultant of E1 and E2 acts along the diagonal in the direction of E3Resultant of E1 and E2, E4=E12+E22=1.67×2×10−7=2.36×10−7N/kgsay ∴Net field E=E3+E4=0.834×10−7+2.36×10−7N/kg net Field E=3.194×10−7=3.2×10−7N/kg