A uniform flexible chain of mass m and length 2 ℓ hangs in equilibrium over a smooth horizontal pin of negligible diameter. One end of the chain is given a small vertical displacement so that the chain slips over the pin. The speed of chain when it leaves pin is-

Question

A uniform flexible chain of mass m and length 2 ℓ hangs in equilibrium over a smooth horizontal pin of negligible diameter. One end of the chain is given a small vertical displacement so that the chain slips over the pin. The speed of chain when it leaves pin is- (A) √2 g ℓ (B) √g ℓ (C) √4 g ℓ (D) √3 g ℓ

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/3e1e5d5597715e94808d02ce9aa52b1f-.png" /> U i = M / 2 g ℓ / 2+ M / 2 g ℓ / 2=( Mg ℓ/2) U f =0 w C =Δ K ( Mg ℓ/2)-0=1 / 2 MV 2=0 V =√ g ℓ m / s

Q. A uniform flexible chain of mass $m$ and length $2 ℓ$ hangs in equilibrium over a smooth horizontal pin of negligible diameter. One end of the chain is given a small vertical displacement so that the chain slips over the pin. The speed of chain when it leaves pin is-

$2 g ℓ$

$g ℓ$

$4 g ℓ$

$3 g ℓ$

$U_{i} = M /2 g ℓ /2 + M /2 g ℓ /2 = \frac{M g ℓ}{2}$
$U_{f} = 0$
$w_{C} = Δ K$
$\frac{M g ℓ}{2} - 0 = 1/2 M V^{2} = 0$
$V = g ℓ m / s$

Q. A uniform flexible chain of mass m and length 2ℓ hangs in equilibrium over a smooth horizontal pin of negligible diameter. One end of the chain is given a small vertical displacement so that the chain slips over the pin. The speed of chain when it leaves pin is-

2gℓ​

gℓ​

4gℓ​

3gℓ​