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Question: Answered & Verified by Expert

Three particles PQ and R are placed on a straight line as shown in the figure. The masses of PQ and R are 3 m , 3 m  and m respectively. The gravitational force on a fourth particle S of mass m is equal to

PhysicsGravitationJEE Main
Options:
  • A 3 Gm 2 2 d 2  in ST direction only
  • B 3 Gm 2 2 d 2  in SQ direction and 3 Gm 2 2 d 2  in SU direction
  • C 3 Gm 2 2 d 2  in SQ direction only
  • D 3 Gm 2 2 d 2  in SQ direction and 3 Gm 2 2 d 2  in ST direction
Solution:
2065 Upvotes Verified Answer
The correct answer is: 3 Gm 2 2 d 2  in SQ direction only


Along the direction parallel to TU 

Net force = G 3 mm 1 2 d 2 cos 30 - Gm 2 4 d 2 cos 60

                = Gm 2 8 d 2 - Gm 2 8 d 2 = 0

Along the direction perpendicular to TU
Net force = G 3 m 2 1 2 d 2 cos 60 + G 3 m 2 3 d 2 + Gm 2 4 d 2 cos 30

                = 3 Gm 2 2 4 d 2 + 3 Gm 2 3 d 2 + 3 Gm 2 8 d 2

                = 3 Gm 2 d 2 1 + 8 + 3 2 4 = 3 Gm 2 2 d 2 along SQ

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