A uniform rod of length l is released from rest such that it rotates about a smooth pivot. The angular speed of the rod when it becomes vertical is

Question

A uniform rod of length l is released from rest such that it rotates about a smooth pivot. The angular speed of the rod when it becomes vertical is (A) 2 √(6 g/7 l) (B) √(6 g/7 l) (C) 2 √(3 g/7 l) (D) √(3 g/7 l)

Tardigrade Admin · Accepted Answer

Δ K+Δ U=0 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/bf32cff497ed60eebf4dd62cb091482f-.png" /> ((1/2) I0 ω2-0)+[-m g (ℓ/4)]=0 ldots (i) I0=(M ℓ2/12)+m((ℓ/4))2=(7/48) m ℓ2 ldots (ii) From (i) and (ii), ω=2 √(6 g/7 ℓ)

Q. A uniform rod of length $l$ is released from rest such that it rotates about a smooth pivot. The angular speed of the rod when it becomes vertical is

$2 \frac{6 g}{7 l}$

$\frac{6 g}{7 l}$

$2 \frac{3 g}{7 l}$

$\frac{3 g}{7 l}$

$Δ K + Δ U = 0$

$(\frac{1}{2} I_{0} ω^{2} - 0) + [- m g \frac{ℓ}{4}] = 0 \dots$ (i)
$I_{0} = \frac{M ℓ ^{2}}{12} + m (\frac{ℓ}{4})^{2} = \frac{7}{48} m ℓ^{2} \dots$ (ii)
From (i) and (ii), $ω = 2 \frac{6 g}{7 ℓ}$

Q. A uniform rod of length l is released from rest such that it rotates about a smooth pivot. The angular speed of the rod when it becomes vertical is

27l6g​​

7l6g​​

27l3g​​

7l3g​​