This category covers problems involving the conservation of angular momentum in isolated systems. Solve questions to see how angular momentum remains constant in different scenarios.
τ = r×F = |i^j^k^4−30−250| = k^(4×5−(−3)×(−2)) = k^(20−6) = 14k^Nm. Magnitude = 14Nm. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 14 Nm. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Formula: Y = m1y1+m2y2+m3y3m1+m2+m3. Masses: 1,2,3kg; y-coordinates: 1,3,2. Y = (1×1)+(2×3)+(3×2)1+2+3 = 1+6+66 = 136≈2.17m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.17 m. 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 = 25×1×(0.8)2 = 0.256kg m2. K = 12Iω2⇒12.8 = 12×0.256×ω2⇒25.6 = 0.256ω2⇒ω2 = 100⇒ω = 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.
Formula: X = m1x1+m2x2+m3x3m1+m2+m3. Masses: 2,4,6kg; x-coordinates: 0,3,1. X = (2×0)+(4×3)+(6×1)2+4+6 = 0+12+612 = 1812 = 1.5m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.5 m. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
The magnitude of torque (τ = rFsinθ) depends on the force magnitude F and the perpendicular distance rsinθ from the pivot to the line of action of the force. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Force and perpendicular distance from the pivot. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
τ = Iα. τ = 20Nm, I = 4kg m2. α = τI = 204 = 5rad/s2. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 5 rad/s². This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
X = (6×2)+(4×8)6+4 = 12+3210 = 4.4. Y = (6×3)+(4×7)6+4 = 18+2810 = 4.6. Distance = (4.4)2+(4.6)2 = 19.36+21.16 = 40.52≈6.36m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 6.36 m. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
τ = r×F = |i^j^k^120−230| = k^(1×3−2×(−2)) = k^(3+4) = 7k^Nm. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 7 Nm. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
For rolling without slipping: v = ωr. v = 2m/s, r = 0.2m. ω = vr = 20.2 = 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.
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.
L = mvr. m = 3kg, v = 4.2m/s, r = 0.7m. L = 3×4.2×0.7 = 8.82kg m2/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 8.82 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.
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.
