Three point masses 9g, 8g and 4g are placed at the vertices A,B,C respectively of an isosceles triangle. What is the magnitude of gravitational field at a point which is the foot of the perpendicular drawn from vertex A on to BC? (AB = AC = 5cm, BC = 8cm).
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a
6.67×10−11dyne/kg
b
6.88×10−8dyne/g
c
9×10−5N/kg
d
4×10−11dyne/g
answer is B.
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Detailed Solution
Value of G in C.G.S = 6.67×10−8dyne cm2/g2 Field at point P is vector sum of fields due to all individual masses.E→P=E→A+E→B+E→C EA=G×932=6.67×10−8×99=6.67×10−8dyne/g EB=G×842=6.67×10−8×816=6.672×10−8dyne/g EC=G×442=6.67×10−8×416=6.674×10−8dyne/g =1.667×10−8dyne/g E→B and E→C act on the same line in opp. Direction since EB>ECThe result of E→B+E→C will be towards B and will have a magnitude EB−EC EB−EC=1.668×10−8dyne/g The net field at point P is E=EA2+EB−EC2 Net gravitational field at P=E=6.67×10−82+1.667×10−82=6.88×10−8dyne/g