A bob of mass $0.1\; kg$ hung from the celling of a room by a string $2 \;m$ long is set into oscillation. The speed of the bob at its mean position is $1\; m s ^{-1}$. What is the trajectory of the bob if the string is cut when the bob is
$(a) $ at one of its extreme positions,
$(b)$ at its mean position.
A bob of mass $0.1\; kg$ hung from the celling of a room by a string $2 \;m$ long is set into oscillation. The speed of the bob at its mean position is $1\; m s ^{-1}$. What is the trajectory of the bob if the string is cut when the bob is
$(a) $ at one of its extreme positions,
$(b)$ at its mean position.
$(a)$ Vertically downward with Parabolic path
At the extreme position, the velocity of the bob becomes zero. If the string is cut at this moment, then the bob will fall vertically on the ground.
$(b)$ At the mean position, the velocity of the bob is $1\; m/s$. The direction of this velocity is tangential to the arc formed by the oscillating bob. If the bob is cut at the mean position, then it will trace a projectile path having the horizontal component of velocity only. Hence, it will follow a parabolic path.
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- [AIPMT 2000]
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