1. When two particles of equal mass revolve about a common centre of mass under their mutual gravitational attraction, the balance between the gravitational force and the centripetal force for circular motion dictates their motion. Since masses are equal, the centre of mass lies at the midpoint on theRead more

    When two particles of equal mass revolve about a common centre of mass under their mutual gravitational attraction, the balance between the gravitational force and the centripetal force for circular motion dictates their motion. Since masses are equal, the centre of mass lies at the midpoint on the line joining the two particles. Each particle revolves about the centre of mass in a circular path of radius R/2.

    The gravitational force between the particles is what furnishes them with the required centripetal force. The gravitational force depends upon the masses of the particles and the distance separating them, which is given by R. On the other hand, centripetal force depends upon the mass of each particle, the orbital speed v, and the radius of their circular path.

    From the equality of gravitational and centripetal forces, it follows that the orbital velocity of each particle is as follows: v = 1/2 √(Gm/R) It follows that speed of each particle is proportional to the square root of the constant of gravitation G and mass of the particle m and inversely proportional to the square root of R. The final expression for the speed is given by v = 1/2 √(Gm/R), which shows the relationship between mass, radius, and speed in this two-body system.

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  2. Gravitational force is one of the fundamental forces of nature that acts between two masses and depends only on the masses and the distance between them. It is governed by Newton's law of gravitation, which states that the gravitational force is proportional to the product of the two masses and inveRead more

    Gravitational force is one of the fundamental forces of nature that acts between two masses and depends only on the masses and the distance between them. It is governed by Newton’s law of gravitation, which states that the gravitational force is proportional to the product of the two masses and inversely proportional to the square of the distance between their centers.

    When two spheres of masses m and M are kept in air, the gravitational force between them is F. It might appear that, if the space surrounding these masses be filled with a liquid of specific gravity 3, then the gravitational force might become affected. Gravitational force does not depend upon the medium surrounding the masses. It’s the universal force, independent on whether the masses are air, water, or even any other medium.

    The specific gravity of the liquid affects only forces of a buoyant nature- that are independent of the actual gravitational attraction. As for buoyancy, it indeed determines an apparent weight, that’s different from the real gravitational attracting each other. Hence for such masses, where one’s space is filled with fluid with specific gravity 3, will not change the amount of gravitational force between it – it remains to be just F.

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  3. The constitutional principle of division of power between the central, state, and local government aligns with the principle of subsidiarity, emphasizing decisions by those most affected and decentralization: - Decentralization: Allows local governments to address local issues independently. - EmpowRead more

    The constitutional principle of division of power between the central, state, and local government aligns with the principle of subsidiarity, emphasizing decisions by those most affected and decentralization:

    – Decentralization: Allows local governments to address local issues independently.
    – Empowerment of Local Authorities: Enables effective decision-making by those closest to the issues.
    – Intervention at Higher Levels: Higher authorities intervene only when lower levels are unable to address certain issues effectively.

    This principle ensures efficient governance, citizen participation, and effective resolution of issues at the most appropriate level.

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  4. (b) an IKEA store in Bengaluru selling products manufactured in China. Explanation: - Interconnected Trade: IKEA, a global brand, showcases globalization by selling products manufactured in China at its Bengaluru store. - Cross-Border Transactions: Goods produced in one country (China) are sold in aRead more

    (b) an IKEA store in Bengaluru selling products manufactured in China.

    Explanation:
    – Interconnected Trade: IKEA, a global brand, showcases globalization by selling products manufactured in China at its Bengaluru store.
    – Cross-Border Transactions: Goods produced in one country (China) are sold in another country (India), illustrating the global flow of products.
    – **International Economic Integration:** This demonstrates how businesses operate beyond national boundaries, highlighting the interconnectedness of economies in a globalized world.

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  5. The quote that BEST reflects the outlook of the masses during the Indian Civil Disobedience Movement is: (a) 'The greatest glory in living lies not in never falling, but in rising every time we fall.' Explanation: - Resilience and Determination: Despite challenges in the Non-Cooperation Movement, InRead more

    The quote that BEST reflects the outlook of the masses during the Indian Civil Disobedience Movement is:

    (a) ‘The greatest glory in living lies not in never falling, but in rising every time we fall.’

    Explanation:
    – Resilience and Determination: Despite challenges in the Non-Cooperation Movement, Indians showed resilience.
    – Perseverance:** The quote highlights the spirit to rise after setbacks, showcasing the people’s determination.
    – Positive Outlook:** It signifies the willingness to continue the struggle despite obstacles, reflecting the masses’ persistent resolve during the Civil Disobedience Movement.

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