Question

The moment of inertiaof a uniform solid sphere of mass m and radius r about a tangent to sphere is

Answer 1

if u don't know about parallax theorem then Google it......
it is only the way to find the moment of inertia at tangent to sphere

Answer 2

Given:

• Sphere has mass m and radius r.

To find:

• Moment of inertia about an axis which is tangent to the sphere ?

Calculation:

• In this of questions, we need to apply THEOREM OF PARALLEL AXES. The net moment of inertia across a parallel axis will be I + md² , where 'd' is the distance of parallel axis from geometric axis.

So, net moment of inertia :

$I_{new} = I_{c} + m {d}^{2}$

• For a tangent, d = r .

$\implies I_{new} = \dfrac{2}{5} m {r}^{2} + m {r}^{2}$

$\implies I_{new} = \dfrac{2 + 5}{5} m {r}^{2}$

$\implies I_{new} = \dfrac{7}{5} m {r}^{2}$

So, the new moment of inertia is 7/5 mr² .