This category focuses on torque, angular momentum, and their conservation principles in rotating systems. Work through problems to understand how forces and motion interact in rotational dynamics.
α = τI = 246 = 4rad/s2. ω = ω0+αt = 0+4×3 = 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 C is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
τ = r×F = |i^j^k^−130520| = k^((−1)×2−3×5) = k^(−2−15) = −17k^Nm. As per NCERT, applying relevant law/formula with correct units and sign convention leads to -17 Nm. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Pulling arms closer reduces the moment of inertia (I). With no external torque, angular momentum (L = Iω) is conserved, so ω increases as I decreases. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Due to conservation of angular momentum. 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 rod pivoted at its center: I = 112ML2. M = 4kg, L = 2.5m. I = 112×4×(2.5)2 = 4×6.2512 = 2512≈2.08kg m2. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.08 kg m². 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 = 2kg, v = 6m/s, r = 0.4m. L = 2×6×0.4 = 4.8kg m2/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.8 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.
v = ωr. v = 3m/s, r = 0.6m. ω = vr = 30.6 = 5rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 5 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.
I = 12MR2 = 12×4×(0.5)2 = 0.5kg m2. K = 12Iω2⇒50 = 12×0.5×ω2⇒100 = 0.5ω2⇒ω2 = 200⇒ω = 200≈14.14rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 14 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.
For a uniform circular ring, the center of mass is at its geometric center. Given center at (3,4), CM position = (3,4). As per NCERT, applying relevant law/formula with correct units and sign convention leads to (3,4). This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
I = MR2 = 6×(0.3)2 = 0.54kg m2. L = Iω = 0.54×5 = 2.7kg m2/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.7 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.
I = MR2 = 4×(0.6)2 = 1.44kg m2. ω = LI = 121.44≈8.33rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 8.33 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.
Angular momentum: L = r×p, where p = mv = 1×(3i^+4j^). L = |i^j^k^020340| = k^(0×4−2×3) = −6k^kgm2/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 B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
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.
