The gravitational intensity at the centre O o | vedclass

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(B) For a complete spherical shell of uniform mass density,the gravitational intensity at any point inside it is zero. This is because the gravitation

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$c$

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(B) For a complete spherical shell of uniform mass density,the gravitational intensity at any point inside it is zero. This is because the gravitational forces exerted by different parts of the shell on a particle at the centre cancel each other out due to symmetry.If we consider a hemispherical shell,we can imagine it as a complete spherical shell from which the upper half has been removed. Let the gravitational intensity due to the complete shell be $I_{total} = 0$. Let $I_{upper}$ be the intensity due to the upper hemisphere and $I_{lower}$ be the intensity due to the lower hemisphere at the centre $O$. Then,$I_{upper} + I_{lower} = 0$,which implies $I_{lower} = -I_{upper}$.The gravitational force (and thus intensity) due to the upper hemisphere at the centre $O$ would be directed downwards (towards the lower hemisphere). Therefore,the intensity due to the lower hemisphere must be directed upwards,towards the missing upper part,to cancel the effect. However,the question asks for the intensity due to the existing hemispherical shell (the lower part). The gravitational force exerted by the lower hemispherical shell on a particle at the centre $O$ is directed towards the mass,i.e.,downwards. Thus,the gravitational intensity at the centre $O$ is directed downwards,which corresponds to arrow $c$.

The gravitational intensity at the centre $O$ of a hemispherical shell of uniform mass density has the direction indicated by which arrow?

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