#coordinate geometry

Vector Product and Rotational Kinematics

A uniform rectangular plate of dimensions 3m×5m and mass 12kg has one corner at (1,1) along the x- and y-axes. What is t

For a uniform rectangle, the center of mass is at the centroid. Vertices: (1,1),(4,1),(1,6),(4,6). CM: X = 1+32 = 2.5, Y = 1+52 = 3.5. Position: (2.5,3.5)m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to (2.5,3.5). 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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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

A uniform square plate of side 6m and mass 9kg has one corner at (2,2) along the x- and y-axes. What is the position of

For a uniform square, the center of mass is at the centroid. Vertices: (2,2),(8,2),(2,8),(8,8). CM: X = 2+62 = 5, Y = 2+62 = 5. Position: (5,5)m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to (5,5). 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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Center of Mass and System of Particles

Two particles of masses 5kg and 3kg are at (0,4) and (8,0) respectively. What is the distance of their center of mass fr

X = (5×0)+(3×8)5+3 = 248 = 3. Y = (5×4)+(3×0)5+3 = 208 = 2.5. Distance = X2+Y2 = 32+(2.5)2 = 9+6.25 = 15.25≈3.9m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.9 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 4kg and 6kg are at (0,7) and (8,3) respectively. What is the distance of their center of mass fr

X = (4×0)+(6×8)4+6 = 4810 = 4.8. Y = (4×7)+(6×3)4+6 = 28+1810 = 4.6. Distance = (4.8)2+(4.6)2 = 23.04+21.16 = 44.2≈6.65m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 6.65 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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