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प्रश्न
A string is wrapped over the edge of a uniform disc and the free end is fixed with the ceiling. The disc moves down, unwinding the string. Find the downward acceleration of the disc.
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उत्तर
Let the radius of the disc be R.
Let the tension in the string be T.
Let the acceleration of the disc be a.
From the free body diagram, we have
\[mg - T = ma ........(1)\]
Torque about the centre of disc,
\[T \times R = I \times \alpha\]
\[\Rightarrow T \times R = \frac{1}{2}m R^2 \times \frac{a}{R}\]
\[ \Rightarrow T = \frac{1}{2}ma ...........(2)\]
Putting this value in equation (1), we get
\[mg - \frac{1}{2}ma = ma\]
\[ \Rightarrow mg = \frac{3}{2}ma\]
\[ \Rightarrow a = \frac{2g}{3}\]
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संबंधित प्रश्न
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Read each statement below carefully, and state, with reasons, if it is true or false;
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Read each statement below carefully, and state, with reasons, if it is true or false;
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Answer in Brief:
A rigid object is rolling down an inclined plane derive the expression for the acceleration along the track and the speed after falling through a certain vertical distance.
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What is the condition for pure rolling?
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An object is rolling without slipping on a horizontal surface and its rotational kinetic energy is two-thirds of translational kinetic energy. The body is ______.
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Solid spherical ball is rolling on a frictionless horizontal plane surface about is axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is ______.
When a sphere rolls without slipping, the ratio of its kinetic energy of translation to its total kinetic energy is ______.
