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प्रश्न
Figure ( following ) shows a smooth track which consists of a straight inclined part of length l joining smoothly with the circular part. A particle of mass m is projected up the incline from its bottom. Assuming that the projection-speed is \[\nu_0\] and that the block does not lose contact with the track before reaching its top, find the force acting on it when it reaches the top.
उत्तर
(b) When the block is projected at a speed:
Let the velocity at C be \[\nu_0\] .
Applying energy principle,
\[\left( \frac{1}{2} \right) \text{m}\nu_0^2 - \left( \frac{1}{2} \right) \text{m}\left( 2 \nu_0 \right)^2 \]
\[ = - \text{mg} \left[ \text{ l } \sin \theta + R \left( 1 - \cos \theta \right) \right]\]
\[ \Rightarrow V^2 = 4 \nu_0^2 - 2g \left[ \text{ l } \sin g \theta + R \left( 1 - \cos \theta \right) \right]\]
\[ = 4 . 2 g \left[ \text{ l } \sin \theta + R \left( 1 - \cos \theta \right) \right] - \]
\[2g \left[ \text{ l } \sin \theta + R \left( 1 - \cos \theta \right) \right]\]
So, force acting on the body,
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