Question

Consider three concentric shells of masses `M_(1),M_(2) and M_(3)` having radii a,b and c respectively are situated as shown in

Gravitational field at a point located at Q and P is
A. `(G(M_(1)+M_(2)))/(y^(2)),(G(M_(1)+M_(2)))/(y^(2))`
B. `(G(M_(1)+M_(2)+M_(3)))/(Y^(2)),(G(M_(1)+M_(2)))/(x^(2))`
C. `(G(M_(1)+M_(2)+M_(3)))/(a^(2)),(GM_(1))/(a^(2))`
D. `(G(M_(1)+M_(2)+M_(3)))/(C^(2)),(GM_(2))/(b^(2))`

Answer 1

Correct Answer - B
Gravitational field at an external point due to spherical shell of mass M is `((GM)/(r^(2)))` while at an internal point is zero
(i) Point Q is external to shell, `M_(1),M_(2) and M_(3)` So, field at Q will be
`E_(Q)=(GM_(1))/(y^(2))+(GM_(2))/(y^(2))+(GM_(3))/(y^(2))=(G)/(y^(2))(M_(1)+M_(2)+M_(3))`
(ii) Field at P will be
`F_(p)=(GM_(1))/(x^(2))+(GM_(2))/(x^(2))+0=(G)/(x^(2))(M_(1)+M_(2))`.