Question

A uniform ring of mass m and radius r is placed directly above a uniform sphere of mass M and of equal radius . The centre of the ring is directly above the centre of the sphere at a distance r square root 3 as shown. The gravitational force exerted by the sphere on the ring will be
(a) GMm/8r? (b) GMm/4r? (c) 13 GMm/8r?" (d) GMm/8r? v3
V34 /2r
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Answer 1

We know

Gravitational force = GM1M2/r^2

where M1 and M2 are mass of two body and r is the distance between two body G is constant

take

M1 = m

M2= M

Since mass is concentrate between the cylinder so

r = 2r

Now

Fg = GMm/4r^2

Answer 2

Answer:

Gravitational field due to ring at a distance

d=3–√Rd=3R on its axis is

E=GMd(R2+d2)3/2E=GMd(R2+d2)3/2

=3–√GM8R2=3GM8R2

Force on the sphere = mass of sphere ×× E

=8ME=8ME

=3–√GM2R2=3GM2R2

Hence d is the correct answer.