Focused practice on vector operations like the cross product and their applications in rotational motion, including angular displacement, velocity, and acceleration.
Angular acceleration (α) is caused by net external torque (τ = Iα), which drives rotational change. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Net external torque. 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^8−30270| = k^(8×7−(−3)×2) = k^(56+6) = 62k^. Magnitude = 62. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 62. 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 uniform triangular lamina, the center of mass is at the centroid, the average of the vertices. X = 0+5+03 = 53≈1.67m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1.67 m. 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^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.
α = τI = 126 = 2rad/s2. Δω = αt = 2×3 = 6rad/s. ω = ω0+Δω = 3+6 = 9rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 9 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.
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.
I = 25MR2 = 25×5×(0.2)2 = 0.08kg m2. ω = LI = 80.08 = 100rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 100 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.
A rigid body is one where the distances between all pairs of particles remain constant, even under the influence of forces. This is an idealization, as real bodies deform slightly, but it’s a key assumption in rotational dynamics.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
For a single object, the center of mass velocity equals the object’s velocity. Magnitude = (−2)2+(3)2 = 4+9 = 13≈3.6m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 3.6 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.
I = 12MR2 = 12×4×(0.2)2 = 0.08kg m2. L = Iω = 0.08×25 = 2kg m2/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2.0 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 uniform rectangle, the center of mass is at the centroid. Vertices: (1,1),(4,1),(1,6),(4,6). CM: X = 1+32 = 2.5, Y = 1+52 = 3.5. Position: (2.5,3.5)m. As per NCERT, applying relevant law/formula with correct units and sign convention leads to (2.5,3.5). This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.
L = Iω. For a sphere: I = 25MR2 = 25×5×(0.3)2 = 0.18kg m2. ω = LI = 90.18 = 50rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 50 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.
