The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be m. Given, the length of the rod is 10 √3 m

Question

The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be m. Given, the length of the rod is 10 √3 m (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/chemistry/232d620e098e56e759340142222c6d00-.png" /> I =( m ℓ2/12)= mk 2 ⇒ k 2=(ℓ2/12) ⇒ k =(ℓ/√12)=(ℓ/2 √3)=(10 √3/2 √3)=5

Q. The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be ________ $m$ . Given, the length of the rod is $103 m$

$I = \frac{m ℓ ^{2}}{12} = m k^{2} \Rightarrow k^{2} = \frac{ℓ ^{2}}{12}$
$\Rightarrow k = \frac{ℓ}{12} = \frac{ℓ}{2 3} = \frac{10 3}{2 3} = 5$

Q. The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be ________m. Given, the length of the rod is 103​m

I=12mℓ2​=mk2⇒k2=12ℓ2​ ⇒k=12​ℓ​=23​ℓ​=23​103​​=5

Q. The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be ________ $m$ . Given, the length of the rod is $103 m$

$I = \frac{m ℓ ^{2}}{12} = m k^{2} \Rightarrow k^{2} = \frac{ℓ ^{2}}{12}$
$\Rightarrow k = \frac{ℓ}{12} = \frac{ℓ}{2 3} = \frac{10 3}{2 3} = 5$