Question

a mass M is placed at point P lies on the axis of a ring of mass M and radius R at a distance R from its Centre the gravitational force on mass M is.(1) GMm/R^2 (2) GMm/2R^2 (3) GMm/√2 R^2(4) GMm/2√2 R^2​

Answer 1

gravitational field due to ring along its axis is given by, $E_g=-\frac{GMx}{(x^2+R^2)^{3/2}}$

where x is separation between point of observation to centre of ring and R is the radius of ring.

so, electric field due to ring along its axis at R distance from its centre , $E_g=-\frac{GM}{2\sqrt{2}R^2}$

now, Force applied on mass m, which is placed R distance from centre of ring = $-mE_g$

so, force = -GMm/2√2R²

here, negative sign indicates force is attractive between them.

so, magnitude of force = GMm/2√2R²

hence, option (4) is correct.

Answer 2

Answer:

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