Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be √x cm. The value of x is

Question

Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be √x cm. The value of x is  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

I cm =(2/5) MR 2 I PQ = I cm + md 2 I PQ =(2/5) mR 2+ m (10 cm )2 For radius of gyration I PQ = mk 2 k 2=(2/5) R 2+(10 cm )2 =(2/5)(5)2+100 =10+100=110 k =√110 cm x =110

Q. Solid sphere $A$ is rotating about an axis $PQ$ . If the radius of the sphere is $5 c m$ then its radius of gyration about $PQ$ will be $x c m$ . The value of $x$ is __

$I_{c m} = \frac{2}{5} M R^{2}$
$I_{PQ} = I_{c m} + m d^{2}$
$I_{PQ} = \frac{2}{5} m R^{2} + m (10 c m)^{2}$
For radius of gyration
$I_{PQ} = m k^{2}$
$k^{2} = \frac{2}{5} R^{2} + (10 c m)^{2}$
$= \frac{2}{5} (5)^{2} + 100$
$= 10 + 100 = 110$
$k = 110 c m$
$x = 110$

Q. Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5cm then its radius of gyration about PQ will be x​cm. The value of x is __

Icm​=52​MR2 IPQ​=Icm​+md2 IPQ​=52​mR2+m(10cm)2 For radius of gyration IPQ​=mk2 k2=52​R2+(10cm)2 =52​(5)2+100 =10+100=110 k=110​cm x=110

Q. Solid sphere $A$ is rotating about an axis $PQ$ . If the radius of the sphere is $5 c m$ then its radius of gyration about $PQ$ will be $x c m$ . The value of $x$ is __

$I_{c m} = \frac{2}{5} M R^{2}$
$I_{PQ} = I_{c m} + m d^{2}$
$I_{PQ} = \frac{2}{5} m R^{2} + m (10 c m)^{2}$
For radius of gyration
$I_{PQ} = m k^{2}$
$k^{2} = \frac{2}{5} R^{2} + (10 c m)^{2}$
$= \frac{2}{5} (5)^{2} + 100$
$= 10 + 100 = 110$
$k = 110 c m$
$x = 110$