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Center of Mass and System of Particles

This category focuses on finding the center of mass and analyzing systems of particles. Work through problems to understand how mass distribution affects motion and stability.

25 questions

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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Center of Mass and System of Particles

A solid cylinder of mass 3kg and radius 0.4m has an angular momentum of 12kg m2/s. What is its angular velocity?

I = 12MR2 = 12×3×(0.4)2 = 0.24kg m2. ω = LI = 120.24 = 50rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 50 rad/s. 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

A solid sphere of mass 4kg and radius 0.3m has an angular momentum of 7.2kg m2/s. What is its angular velocity?

I = 25MR2 = 25×4×(0.3)2 = 0.144kg m2. ω = LI = 7.20.144 = 50rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 50 rad/s. 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

A torque of 18Nm acts on a disk with moment of inertia 6kg m2 starting from rest. What is its angular speed after 4s?

α = τI = 186 = 3rad/s2. ω = ω0+αt = 0+3×4 = 12rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 12 rad/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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Center of Mass and System of Particles

A 2kg particle moves with velocity v\=5i^−2j^m/s at r\=3j^m. What is the z-component of its angular momentum?

L = r×p = |i^j^k^0305−20| = k^(0×(−2)−3×5) = −15k^kg m2/s. Z-component = −15kg m2/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -15 kg m²/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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Center of Mass and System of Particles

A force F\=4i^−6j^N acts at r\=5i^+2j^m. What is the magnitude of the torque about the origin?

τ = r×F = |i^j^k^5204−60| = k^(5×(−6)−2×4) = k^(−30−8) = −38k^Nm. Magnitude = 38Nm. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 38 Nm. 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

A cylinder of mass 10kg and radius 0.5m rolls without slipping. If its angular momentum about its axis is 25kg m2/s, wha

Angular momentum: L = Iω. For a solid cylinder: I = 12MR2 = 12×10×(0.5)2 = 1.25kgm2. ω = LI = 251.25 = 20rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 20 rad/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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Center of Mass and System of Particles

A 1kg mass rotates in a circle of radius 0.5m with a speed of 4m/s. What is its angular momentum about the center?

L = mvr. m = 1kg, v = 4m/s, r = 0.5m. L = 1×4×0.5 = 2kg m2/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2 kg m²/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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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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