This category covers the calculation and application of moment of inertia and radius of gyration for rigid bodies. Learn how mass distribution affects rotational motion through solved problems and theory.
The motion of any point is a combination of the translational velocity of the body (same for all points) and the rotational velocity about the axis, varying with distance from the axis.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
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.
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.
For a disk, I = 12MR2. Doubling R increases R2 by a factor of 4, so I increases by a factor of 4 if M is constant. As per NCERT, applying relevant law/formula with correct units and sign convention leads to It quadruples. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
For a uniform square, the center of mass is at the centroid. Vertices: (0,0),(4,0),(0,4),(4,4). CM: X = 0+42 = 2, Y = 0+42 = 2. Position: (2,2)m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to (2,2). This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
α = τI = 168 = 2rad/s2. Δω = αt = 2×3 = 6rad/s. ω = ω0+Δω = 2+6 = 8rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 8 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.
I = 25MR2 = 25×2×(0.6)2 = 0.288kg m2. K = 12Iω2 = 12×0.288×(5)2 = 0.144×25 = 3.6J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.6 J. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
a×b = |i^j^k^630−420| = k^(6×2−3×(−4)) = k^(12+12) = 24k^. Magnitude = 24. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 24. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
α = τI = 105 = 2rad/s2. Δω = αt = 2×5 = 10rad/s. ω = ω0+Δω = 3+10 = 13rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 13 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.
τ = r×F = |i^j^k^−210730| = k^((−2)×3−1×7) = k^(−6−7) = −13k^Nm. Magnitude = 13Nm. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 13 Nm. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
L = r×p = |i^j^k^0206−40| = k^(0×(−4)−2×6) = −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.
α = τI = 255 = 5rad/s2. ω = ω0+αt = 0+5×2 = 10rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 10 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.
