#two particles

Rotational Motion Applications

Two particles of masses 4kg and 6kg are at (2,0) and (0,3) respectively. What is the distance of their center of mass fr

X = (4×2)+(6×0)4+6 = 810 = 0.8. Y = (4×0)+(6×3)4+6 = 1810 = 1.8. Distance = (0.8)2+(1.8)2 = 0.64+3.24 = 3.88≈1.97m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.97 m. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Rotational Motion Applications

Two particles of masses 2kg and 8kg are at (1,5) and (4,1) respectively. What is the distance of their center of mass fr

X = (2×1)+(8×4)2+8 = 2+3210 = 3.4. Y = (2×5)+(8×1)2+8 = 10+810 = 1.8. Distance = (3.4)2+(1.8)2 = 11.56+3.24 = 14.8≈3.85m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.85 m. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Center of Mass and System of Particles

Two particles of masses 7kg and 3kg are at (0,6) and (5,0) respectively. What is the distance of their center of mass fr

X = (7×0)+(3×5)7+3 = 1510 = 1.5. Y = (7×6)+(3×0)7+3 = 4210 = 4.2. Distance = (1.5)2+(4.2)2 = 2.25+17.64 = 19.89≈4.46m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.46 m. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Torque and Angular Momentum

A system of two particles, 3kg at (1,2) and 1kg at (5,6), moves as a rigid body. What is the distance of the center of m

X = (3×1)+(1×5)3+1 = 3+54 = 2. Y = (3×2)+(1×6)3+1 = 6+64 = 3. Distance = X2+Y2 = 22+32 = 4+9 = 13≈3.6m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.6 m. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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