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AIIMS 2012
Exam
AIIMS
Year
2012
Subject
Physics
Chapter
Rotational Motion

AIIMS 2012 · Physics · Rotational Motion

A solid cylinder, a circular disc, a solid sphere and a hollow...

A solid cylinder, a circular disc, a solid sphere and a hollow cylinder of the same radius are placed on an inclined plane. Which of the following will have maximum acceleration at the bottom of the plane?A solid cylinder, a circular disc, a solid sphere and a hollow cylinder of the same radius are placed on an inclinedA solid cylinder, a circular disc, a solid sphere and a hollow cylinder of the same radius are placed on an inclinedA solid cylinder, a circular disc, a solid sphere and a hollow cylinder of the same radius are placed on an inclinedA solid cylinder, a circular disc, a solid sphere and a hollow cylinder of the same radius are placed on an inclinedA solid cylinder, a circular disc, a solid sphere and a hollow cylinder of the same radius are placed on an inclined

Options

  1. ACircular disc.
  2. BSolid cylinder.
  3. CSolid sphere.
  4. DHollow cylinder.

Correct answer

C. Solid sphere.

Step-by-step solution

Let the inclination of the inclined plane be θ\theta. Acceleration of a rolling body is given as A solid cylinder, a circular disc, a solid sphere and a hollow cylinder of the same radius are placed on an inclined
a=gsin⁡θ(1+K2/R2)a=\frac{g \sin \theta}{\left(1+K^2 / R^2\right)} Here, KK is radius of gyration. For circular disc I=12MR2∴K2R2=12I=\frac{1}{2} M R^2 \quad \therefore \frac{K^2}{R^2}=\frac{1}{2} ∴a=23gsin⁡θ\therefore \quad a=\frac{2}{3} g \sin \thetaA solid cylinder, a circular disc, a solid sphere and a hollow cylinder of the same radius are placed on an inclined
For solid cylinder I=12MR2∴K2R2=12I=\frac{1}{2} M R^2 \therefore \frac{K^2}{R^2}=\frac{1}{2} ∴a=23gsin⁡θ\therefore \quad a=\frac{2}{3} g \sin \thetaA solid cylinder, a circular disc, a solid sphere and a hollow cylinder of the same radius are placed on an inclined
For solid sphere I=25MR2∴K2R2=25I=\frac{2}{5} M R^2 \therefore \frac{K^2}{R^2}=\frac{2}{5} ∴a=57gsin⁡θ\therefore \quad a=\frac{5}{7} g \sin \thetaA solid cylinder, a circular disc, a solid sphere and a hollow cylinder of the same radius are placed on an inclined
For hollow cylinder I=MR2∴K2R2=1I=M R^2 \quad \therefore \frac{K^2}{R^2}=1 ∴a=12gsin⁡θ\therefore a=\frac{1}{2} g \sin \thetaA solid cylinder, a circular disc, a solid sphere and a hollow cylinder of the same radius are placed on an inclined
Hence, from (i), (ii), (iii) and (iv) we conclude that the solid sphere will reach the bottom with maximum acceleration.
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