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#vector components

9 public questions tagged with this topic.

Vector Product and Rotational Kinematics

A 4kg block moves with a velocity of −2i^+3j^m/s. What is the magnitude of the velocity of its center of mass?

For a single object, the center of mass velocity equals the object’s velocity. Magnitude = (−2)2+(3)2 = 4+9 = 13≈3.6m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.6 m/s. 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

A 6kg object moves with a velocity of 3i^−2j^m/s. What is the magnitude of the velocity of its center of mass?

For a single object, the center of mass velocity equals the object’s velocity. Magnitude = (3)2+(−2)2 = 9+4 = 13≈3.6m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.6 m/s. 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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Rigid Body Motion and Equilibrium

Two vectors are given as a\=2i^+3j^ and b\=−3i^+4j^. What is the magnitude of their vector product a×b?

a×b = |i^j^k^230−340| = k^(2×4−3×(−3)) = k^(8+9) = 17k^. Magnitude = |a×b| = 17. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 17. 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 5kg object moves with a velocity of 4i^+2j^m/s. What is the magnitude of the velocity of its center of mass?

For a single object, the center of mass velocity equals the object’s velocity. Magnitude = (4)2+(2)2 = 16+4 = 20≈4.47m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.47 m/s. 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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