System of Particles and Rotational Motion
- In a rectangle ABCD (BC = 2 AB). The moment of inertia is minimum along axis through
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The M.I. is minimum about EG because mass distribution is at minimum distance from EG.
Correct Option: D
The M.I. is minimum about EG because mass distribution is at minimum distance from EG.
- ABC is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. IAB, IBC and ICA are the moments of inertia of the plate about AB, BC and CA as axes respectively. Which one of the following relations is correct?
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The intersection of medians is the centre of mass of the triangle. Since distances of centre of mass from the sides are related as : xBC > xAB > xAC , therefore, IBC > IAB > IAC or IBC > IAB.
Correct Option: B
The intersection of medians is the centre of mass of the triangle. Since distances of centre of mass from the sides are related as : xBC > xAB > xAC , therefore, IBC > IAB > IAC or IBC > IAB.
- If a sphere is rolling, the ratio of the translational energy to total kinetic energy is given by
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E = Et + Er = 1 mv² + 1 Iω² 2 2 = 1 mv² + 1 × 
2 mr² 
ω² 2 2 5 = 1 mv² + 1 mv² = 7 mv² 2 5 10 ∴ = 1 mv² Et 2 E 7 mv² 10 = 5 7
Correct Option: D
E = Et + Er = 1 mv² + 1 Iω² 2 2 = 1 mv² + 1 × 2 mr² ω² 2 2 5 = 1 mv² + 1 mv² = 7 mv² 2 5 10 ∴ = 1 mv² Et 2 E 7 mv² 10 = 5 7
- There is a flat uniform triangular plate ABC such that AB = 4 cm, BC = 3 cm and angle ABC = 90º. The moment of inertia of the plate about AB, BC and CA as axis is respectively I1, I2 and I3. Which one of the following is true?
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Moment of Inertia depend upon mass and distribution of masses as I = Σmr².
Further, as the distance of masses is more , more is the moment of Inertia.
If we choose BC as axis. Distance is maximum. Hence, Moment of Inertia is maximum.
∴ I2 > I1, I2 > I3Correct Option: B
Moment of Inertia depend upon mass and distribution of masses as I = Σmr².
Further, as the distance of masses is more , more is the moment of Inertia.
If we choose BC as axis. Distance is maximum. Hence, Moment of Inertia is maximum.
∴ I2 > I1, I2 > I3
- A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be
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Rotational energy = 1 l(ω)² = 1 (mK²)ω² 2 2 Linear kinetic energy = 1 (mK²)ω 2 ∴ Required fraction = 1 (mK²)ω 2 1 (mK²)ω + 1 mω²R² 2 2 = K² K² + R² Correct Option: D
Rotational energy = 1 l(ω)² = 1 (mK²)ω² 2 2 Linear kinetic energy = 1 (mK²)ω 2 ∴ Required fraction = 1 (mK²)ω 2 1 (mK²)ω + 1 mω²R² 2 2 = K² K² + R²
