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Force on a particle from a sphere with a spherical cavity

This type of question, asked 2 times: 2021 Paper 3, 22 Jan 2025. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 3

    2
    A solid sphere of radius RR gravitationally attracts a particle placed at 3R3R from its centre with a force F1F_{1}. Now a spherical cavity of radius (R2)\left( \frac{R}{2} \right) is made in the sphere (as shown in figure) and the force becomes F2F_{2}. The value of F1:F2F_{1}:F_{2} is:

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  2. Question 2

    22 Jan 2025

    13
    A small point of mass mm is placed at a distance 2R2R from the centre ' OO ' of a big uniform solid sphere of mass M and radius R . The gravitational force on ' mm ' due to MM is F1F_{1}. A spherical part of radius R/3R/3 is removed from the big sphere as shown in the figure and the gravitational force on mm due to remaining part of M is found to be F2F_{2}. The value of ratio F1:F2F_{1}:F_{2} is

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