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Q.

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
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