This category includes problems on rotational kinetic energy, work done by torque, and energy conservation in rotating systems. Solve questions to see how energy transforms in rotational motion.
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.
From τ = Iα, angular acceleration α is inversely proportional to moment of inertia I. A larger I means more resistance to rotation, reducing α for the same torque. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Because it resists angular acceleration more. 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 single object, the center of mass velocity equals the object’s velocity. Magnitude = (−5)2+(−2)2 = 25+4 = 29≈5.39m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 5.39 m/s. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
v = ωr. ω = 12rad/s, r = 0.25m. v = 12×0.25 = 3m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.0 m/s. 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^5−40360| = k^(5×6−(−4)×3) = k^(30+12) = 42k^. Magnitude = 42. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 42. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Linear velocity v = ωr increases with distance r from the axis because angular velocity ω is constant for a rigid body, and v is directly proportional to r. As per NCERT, applying relevant law/formula with correct units and sign convention leads to It increases. 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 = 5×(0.5)2 = 1.25kg m2. ω = LI = 12.51.25 = 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 C is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
v = ωr. ω = 8rad/s, r = 0.4m. v = 8×0.4 = 3.2m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.2 m/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 = Iω) is a measure of rotational motion, while torque (τ = r×F) is the cause of rotational change. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Angular momentum measures rotational motion, torque causes it. 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 = 4×(0.3)2 = 0.36kg m2. K = 12Iω2 = 12×0.36×(8)2 = 0.18×64 = 11.52J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 11.52 J. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
Moment of inertia (I) measures rotational inertia, reflecting how mass is distributed relative to the axis and the body’s resistance to angular acceleration. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Moment of inertia. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
For a symmetric rigid body rotating about a fixed axis (a symmetry axis), the perpendicular components of angular momentum cancel out due to symmetry, leaving L = Iω aligned with the axis.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
