Question

the moment of inertia of 100 kg sphere of 50 cm diameter is​

Answer 1

The moment of inertia of a sphere

Answer 2

Given-

☛Mass of sphere = 100kg

☛Diameter = 50cm i.e, radius = 25cm

   

Find-

• Moment of inertia-?

     

Formula to be used-

Moment of inertia of a sphere is given by

$\boxed{ \sf{ I = \dfrac{2}{5} mr^2}}$

where,

I= Moment of inertia

m= mass

r= radius

       

Solution-

☛At first Change radius cm to m

we know 1 m= 100 cm

$\sf{\implies 1cm= \dfrac{1}{100}m}$

$\sf {\implies 25cm= \dfrac{25}{100}m = 0.25m}$

Radius = 0.25m

☛Put the given values in the formula,

$\sf{\implies I = \dfrac{2}{5} \times 100 \times 0.25^2 }$

$\sf{\implies I= 2\times 20 \times 0.0625 }$

$\sf{\implies I = 2.5}$

           

Therefore, Moment of inertia of sphere is 2.5kgm².