Question

The moment of inertia of a square plate of
mass 4 kg and side 1 m about an axis
passing through its centre and
perpendicular to its plane is
0.33 kg m?

0.67 kg m/s2

0.17 kg m/s2

0.247 kg m/s2​

Answer 1

Explanation:

7ऊ chi chi construction L chi dfi chi u.c fti it

Answer 2

Given:

A square plate of mass 4 kg and side 1 m.

To find:

The moment of inertia of a square plate about an axis passing through its centre and perpendicular to its plane is ?

Calculation:

General expression for rectangular plate about an axis perpendicular to plane and through the centre is :

$\boxed{ \therefore \: I = \dfrac{m( {a}^{2} + {b}^{2} )}{12} }$

For a square , a = b = edge length :

$\implies\: I = \dfrac{m( {l}^{2} + {l}^{2} )}{12}$

$\implies\: I = \dfrac{m(2 {l}^{2} )}{12}$

$\implies\: I = \dfrac{m{l}^{2} }{6}$

$\implies\: I = \dfrac{4 \times {(1)}^{2} }{6}$

$\implies\: I = \dfrac{4 }{6}$

$\implies\: I = \dfrac{2 }{3}$

$\implies\: I = 0.67 \: kg {m}^{2}$

So, the required Moment Of Inertia is 0.67 kgm².