wiz-icon
MyQuestionIcon
MyQuestionIcon
2
You visited us 2 times! Enjoying our articles? Unlock Full Access!
Question

Four particles having masses m,2m,3m and 4m are placed at the four corners of a square of edge a.

Find gravitational force acting on a particle of mass m place at the center.

Open in App
Solution

Gravitational force on mass 'm' at center is
Fx^i+Fx^j=F=G×m×m(a2)2+G×m×2m(a2)2+G×m×3m(a2)2+G×m×4m(a2)2

[Note that above is vector sum]
F1=2Gm2a2;F2=4Gm2a2;F3=6Gm2a2;F4=8Gm2a2

By resolving the force along x-direction,
Fx=(F2cos45°+F3cos45°)(F1cos45°+F4cos45)Fx=(10Gm2a210Gm2a2)×cos45°=0

By resolving the force along y-direction,
Fy=[(F1+F2)(F4+F3)]sin45°=[6Gm2a214Gm2a2]sin45°=7m22a2

Net force on m(at center) is (7m22a2)^j [along negative y-direction]

984613_1017865_ans_f517cf3fba05430282bfec3aeb4acaeb.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Kepler's Law
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon