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Question

A uniform solid sphere of mass M and radius a is surrounded symmetrically by a uniform thin spherical shell of equal mass and radius 2 a. the ratio of gravitational field at a distance 32 a froth the centre to 52 a from the centre is..


A

2518

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B

1619

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C

259

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D

1

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Solution

The correct option is A

2518


Figure shows the situation. The point P1 is at a distance 32 a from the centre and P2 is at a distance52 from the centre. As P1 is inside the cavity of the thin spherical shell, the field here due to the shell is zero. The field due to the solid sphere is

E= GM(32a)2 = 4GM9a2 .................(1)

This is also the resultant field. The direction is towards the centre. The point P2 is outside the

sphere as well as the shell. Both may be replaced by single particles of the same mass at

the centre. The field due to each of them is

E= GM(52a)2 = 4GM25a2

The resultant field is E=2E'=8GM25a2..........(2) towards the centre.


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