#particle motion

Wave Equation and Displacement Relation

A wave on a string has an amplitude of 0.02 m and a period of 0.01 s. What is the maximum transverse speed of a particle

**Wave equation** y(x,t) = A sin(kx - ωt + φ) describes displacement of progressive harmonic wave, where k = 2π/λ wave number (rad/m), ω = 2πf angular frequency (rad/s), v = ω/k wave speed (m/s). Sign of ωt indicates direction, amplitude A is maximum displacement. ω = (2π/T) = (2π/0.01) = 200π rad/s . Max speed: vₘₐₓ = a ω = 0.02 × 200π ≈ 12.57 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 12.6 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Wave Equation and Displacement Relation

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Moment of Inertia and Radius of Gyration

A 6kg particle moves with velocity v\=3j^m/s at r\=−4i^m. What is the magnitude of its angular momentum about the origin

L = r×p = |i^j^k^−400030| = k^((−4)×3−0×0) = −12k^kg m2/s. Magnitude = 12kg m2/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 12 kg m²/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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Moment of Inertia and Radius of Gyration

A 4kg particle moves with velocity v\=3i^+5j^m/s at r\=−2i^m. What is the z-component of its angular momentum?

L = r×p = |i^j^k^−200350| = k^((−2)×5−0×3) = −10k^kg m2/s. Z-component = −10kg m2/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -10 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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Vector Product and Rotational Kinematics

A 3kg particle moves with velocity v\=6i^m/s at r\=2j^m. What is the magnitude of its angular momentum about the origin?

L = r×p = |i^j^k^020600| = k^(0×0−2×6) = −12k^kg m2/s. Magnitude = 12kg m2/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 12 kg m²/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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Vector Product and Rotational Kinematics

A 4kg particle moves with velocity v\=−5i^+2j^m/s at r\=3i^m. What is the z-component of its angular momentum?

L = r×p = |i^j^k^300−520| = k^(3×2−0×(−5)) = 6k^kg m2/s. Z-component = 6kg m2/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 6 kg m²/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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Conservation of Angular Momentum

A 2kg particle moves with velocity v\=−5i^−3j^m/s at r\=4i^m. What is the z-component of its angular momentum?

L = r×p = |i^j^k^400−5−30| = k^(4×(−3)−0×(−5)) = −12k^kg m2/s. Z-component = −12kg m2/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -12 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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Conservation of Angular Momentum

A 4kg particle moves with velocity v\=−2j^m/s at r\=5i^m. What is the magnitude of its angular momentum about the origin

L = r×p = |i^j^k^5000−20| = k^(5×(−2)−0×0) = −10k^kg m2/s. Magnitude = 10kg m2/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 10 kg m²/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 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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Rotational Kinetic Energy and Dynamics

A 2kg particle moves with velocity v\=4i^+5j^m/s at r\=−3j^m. What is the z-component of its angular momentum?

L = r×p = |i^j^k^0−30450| = k^(0×5−(−3)×4) = 12k^kg m2/s. Z-component = 12kg m2/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 12 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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Rotational Kinetic Energy and Dynamics

A 3kg particle moves with velocity v\=−4j^m/s at r\=6i^m. What is the magnitude of its angular momentum about the origin

L = r×p = |i^j^k^6000−40| = k^(6×(−4)−0×0) = −24k^kg m2/s. Magnitude = 24kg m2/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 24 kg m²/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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Rotational Kinetic Energy and Dynamics

A 5kg particle moves with velocity v\=2i^−3j^m/s at r\=4j^m. What is the z-component of its angular momentum?

L = r×p = |i^j^k^0402−30| = k^(0×(−3)−4×2) = −8k^kg m2/s. Z-component = −8kg m2/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -8 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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Torque and Angular Momentum

A 4kg particle moves with velocity v\=3j^m/s at r\=2i^m. What is the magnitude of its angular momentum about the origin?

L = r×p = |i^j^k^200030| = k^(2×3−0×0) = 6k^kg m2/s. Magnitude = 6kg m2/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 6 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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