If the moment of inertia of a solid sphere of mass M and radius R about an axis passing through its centre of mass is (2/5) MR2 , then its radius of gyration about an axis which is parallel to given axis and at a distance 2R from the center will be

Question

If the moment of inertia of a solid sphere of mass M and radius R about an axis passing through its centre of mass is (2/5) MR2 , then its radius of gyration about an axis which is parallel to given axis and at a distance 2R from the center will be (A) R √(22/5) (B) R √(26/3) (C) R √(26/5) (D) R √(11/5)

Tardigrade Admin · Accepted Answer

I = (2/5)MR2+M(2R)2 ⇒ Mk2 = (22MR2/5)⇒ k = R √(22/5)

Q. If the moment of inertia of a solid sphere of mass M and radius R about an axis passing through its centre of mass is $\frac{2}{5} M R^{2}$ , then its radius of gyration about an axis which is parallel to given axis and at a distance 2R from the center will be

$R \frac{22}{5}$

$R \frac{26}{3}$

$R \frac{26}{5}$

$R \frac{11}{5}$

$I = \frac{2}{5} M R^{2} + M (2 R)^{2}$
$\Rightarrow M k^{2} = \frac{22 M R ^{2}}{5} \Rightarrow k = R \frac{22}{5}$

Q. If the moment of inertia of a solid sphere of mass M and radius R about an axis passing through its centre of mass is 52​MR2 , then its radius of gyration about an axis which is parallel to given axis and at a distance 2R from the center will be

R522​​

R326​​

R526​​

R511​​