System of Particles & Rotatory Motion

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The centre of mass (CM) is the point where the entire mass of a system can be considered to be concentrated for the purpose of analyzing translational motion. It is the average position of all the mas…

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Let the 2 kg mass be at origin (x₁ = 0), and 3 kg at x₂ = 10 m. Formula: X_cm = (m₁x₁ + m₂x₂) / (m₁ + m₂) Step 1: X_cm = (2×0 + 3×10) / (2+3) = 30 / 5 = 6 m Answer: 6 m from the 2 kg mass.

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The centre of mass simplifies the motion of extended bodies. Even if different parts move differently, the CM moves as if all external forces act directly on it. For example, a spinning cricket ball f…

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Place square in xy-plane with corners at (0,0), (1,0), (1,1), (0,1). X_cm = (1×0 + 2×1 + 3×1 + 4×0)/(1+2+3+4) = (0+2+3+0)/10 = 5/10 = 0.5 m Y_cm = (1×0 + 2×0 + 3×1 + 4×1)/10 = (0+0+3+4)/10 = 7/10 = …

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Yes, the centre of mass can lie outside the physical body. Examples: 1. A uniform ring – CM is at the geometric centre, where there is no material. 2. A hollow hemisphere – CM lies outside the curved…

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Centre of mass depends only on mass distribution and exists even without gravity. Centre of gravity is the point where total weight acts. For small, uniform objects in uniform gravity, they coincide.

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A rigid body is an idealized object in which the distance between any two particles remains constant, even under external forces. Real objects deform slightly, but we treat them as rigid when deformat…

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No, a heap of sand cannot be considered a rigid body because the relative positions of its particles change easily under small forces. When disturbed, sand flows and deforms, violating the condition o…