Vertical Circular Motion: Practice Problem & Solution
A particle of mass \(m\) is tied to a string of length \(L\) and rotated in vertical circle about other end with critical speed so that it is just able to complete the vertical loop. Then tension in string, when string is at horizontal position will be:
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Vertical Circular Motion. Understanding the underlying formula is key to arriving at the correct answer below:
To just complete the vertical loop, the velocity at the bottom is \(\sqrt{5gL}\). By energy conservation, the velocity at the horizontal position is \(v = \sqrt{3gL}\). The tension at this point is \(T = \frac{mv^2}{L} = 3mg\).
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