#y-coordinate

Conservation of Angular Momentum

Three particles of masses 1kg, 2kg, and 3kg are located at (1,1), (2,3), and (4,2) respectively. What is the y-coordinat

Formula: Y = m1y1+m2y2+m3y3m1+m2+m3. Masses: 1,2,3kg; y-coordinates: 1,3,2. Y = (1×1)+(2×3)+(3×2)1+2+3 = 1+6+66 = 136≈2.17m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.17 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

Three particles of masses 4kg, 8kg, and 12kg are at (1,0), (3,2), and (0,4) respectively. What is the y-coordinate of th

Formula: Y = m1y1+m2y2+m3y3m1+m2+m3. Masses: 4,8,12kg; y-coordinates: 0,2,4. Y = (4×0)+(8×2)+(12×4)4+8+12 = 0+16+4824 = 6424 = 2.67m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.67 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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Moment of Inertia and Radius of Gyration

A system consists of two particles: 1kg at (2,3) and 2kg at (4,1). What is the y-coordinate of the center of mass?

Formula: Y = m1y1+m2y2m1+m2. m1 = 1kg, y1 = 3; m2 = 2kg, y2 = 1. Y = (1×3)+(2×1)1+2 = 3+23 = 53≈1.67m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.67 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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Moment of Inertia and Radius of Gyration

Four particles of masses 1kg, 3kg, 5kg, and 7kg are at (0,0), (2,0), (0,3), and (2,3) respectively. What is the y-coordi

Formula: Y = m1y1+m2y2+m3y3+m4y4m1+m2+m3+m4. Masses: 1,3,5,7kg; y-coordinates: 0,0,3,3. Y = (1×0)+(3×0)+(5×3)+(7×3)1+3+5+7 = 0+0+15+2116 = 3616 = 2.25m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.25 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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Vector Product and Rotational Kinematics

Three particles of masses 2kg, 4kg, and 8kg are at (0,3), (4,0), and (2,5) respectively. What is the y-coordinate of the

Formula: Y = m1y1+m2y2+m3y3m1+m2+m3. Masses: 2,4,8kg; y-coordinates: 3,0,5. Y = (2×3)+(4×0)+(8×5)2+4+8 = 6+0+4014 = 4614≈3.29m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.29 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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