A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at 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 its velocity as it reaches a position where the string is horizontal is (assume g as acceleration due to gravity)

Question

A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at 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 its velocity as it reaches a position where the string is horizontal is (assume g as acceleration due to gravity) (A) √u2 - 2 g L (B) √2 g L (C) √u2 - g L (D) √2 (u2 - g L)

Tardigrade Admin · Accepted Answer

From energy conservation v2=u2-2gL ...(1) Now since the two velocity vectors shown in figure are mutually perpendicular, hence the magnitude of change of velocity will be given by |Δ overset arrow v |=√u2 + v2 <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-7fx72pl9s2feynz6.jpg" /> Substituting value of v2 from Eq.(1) |Δ overset arrow v |=√u2 + u2 - 2 g L |Δ overset arrow v |=√2 (u2 - g L)

$u^{2} - 2 gL$

$2 gL$

$u^{2} - gL$

$2 (u^{2} - gL)$

u2−2gL​

2gL​

u2−gL​

2(u2−gL)​

$u^{2} - 2 gL$

$2 gL$

$u^{2} - gL$

$2 (u^{2} - gL)$