A stone tied to a string of length `L` is whirled in a vertical circle with the ofter end of the string at the centre . At a certin instant of time , the stone is at its lowest position , and has a speed is , the magintube of the change in its velocity as it reached a positive when the string is horizontal is

Options

A. `sqrt(u^(2) - 2gL)`
B. `sqrt(2gL)`
C. `(u^(2) - gL)`
D. `sqrt(2(u^(2) - 2gL)`

Answer

D

Explanation

(d) Appling the principle of conservation of energy `(K.E) _(B) + (P.E)_(p) = K.E)_(A) + (P.E)_(A)`
we get
` (1)/(2) mv^(2) + mgL = (1)/(2) mu^(2)`
Heance, v = sqrt(u^(2) - 2gL) `…(i)
Change is velocity `[barV - barM] = sqrt(v^(2) + u^(2))`
` = sqrt(2(u^(2) - gl)) ` [from]