A spherical hole is made in a solid sphere of radius R. The mass of the sphere before hollowing was M. The gravitational field at the centre of the hole due to the remaining mas is

Zero

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Solution

The correct option is C

By the principle of superposition of fields

$_{E}^{\to} =_{E_{1}}^{\to} +_{E_{2}}^{\to} =$

Here $_{E}^{\to}$ = net field at the centre of hole due to entire mass

$_{E_{1}}^{\to}$ = field due to remaining mass

and $_{E_{2}}^{\to}$ = field due to mass in hole = 0

$∴ E_{1} = E = (\frac{G M}{R^{3}}) . r w h e r e r = \frac{R}{2} ∴ E = \frac{G M}{2 R^{2}}$

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A spherical hole is made in a solid sphere of radius R. The mass of the sphere before hollowing was M. The gravitational field at the centre of the hole due to the remaining mas is

The correct option is C By the principle of superposition of fields →E=→E1+→E2= Here →E = net field at the centre of hole due to entire mass →E1 = field due to remaining mass and →E2 = field due to mass in hole = 0 ∴E1=E=(GMR3).r where r=R2∴E=GM2R2