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Q.

A spherical shell is cut into two pieces along a chord as shown in the figure. P is a point on the plane of the chord. The gravitational field at P due to the upper part is I₁ and that due to the lower part is I₂. What is the relation between them?
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a

$I_{1} > I_{2}$

b

$I_{1} = I_{2}$

c

$I_{1} < I_{2}$

d

no definite relation

answer is C.

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Detailed Solution

At point P, we have $I_{1} - I_{2} = 0$ (because the gravitational field inside a shell is zero). Hence, $I_{1} = I_{2}$ .

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A spherical shell is cut into two pieces along a chord as shown in the figure. P is a point on the plane of the chord. The gravitational field at P due to the upper part is I1 and that due to the lower part is I2. What is the relation between them?