A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. 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

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 centre. 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 (A)  √2(u2-gl)  (B)  √u2-gl  (C)  √u2-2gl  (D)  √2gl

Tardigrade Admin · Accepted Answer

From energy conservation v2=u2-2 g L ....(i) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/41e9bb78b973ba92dd94b8851837b7c9-.png" /> Now, since the two velocity vectors shown in figure are mutually perpendicular, hence the magnitude of change of velocity will be given by |Δ v |=√u2+v2 Substituting value of v2 from Eq.(i), we get |Δ v |=√u2+u2-2 g L =√2(u2-g L)

$2 (u^{2} - g l)$

$u^{2} - g l$

$u^{2} - 2 g l$

$2 g l$

2(u2−gl)​

u2−gl​

u2−2gl​

2gl​

From energy conservation v2=u2−2gL....(i) Now, since the two velocity vectors shown in figure are mutually perpendicular, hence the magnitude of change of velocity will be given by ∣Δv∣=u2+v2​ Substituting value of v2 from Eq.(i), we get ∣Δv∣=u2+u2−2gL​ =2(u2−gL)​

$2 (u^{2} - g l)$

$u^{2} - g l$

$u^{2} - 2 g l$

$2 g l$