A stone is tied to a string of length λ and is whirled in a vertical circle with the other end of the string as the center. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is :
Text Solution
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Key Idea: When stone reaches a position where string is horizontal, it attains the energy partially as kinetic and partially as potential.
When stone is at its lowest position, it has only kinetic energy, given by
k = 
mu 2
At the horizontal position, it has energy
E = U + K = 
mu' 2 + mg λ
According to conservation of energy,
K = E
∴ 
mu2 = 
mu' 2 + mg λ
or 
mu' 2 = 
mu 2 – mg λ
or u' 2 = u 2 – 2g λ
or u' = 
… (i)
So, the magnitude of change in velocity
| Δ 
| = | 
| = 
| Δ 
| = 
= 
[from Eq. ]
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