Question

Two discs having moment of inertia I₁ and I₂ are made from same material have same mass. Their thickness and radii are t₁, t_2, and R₁, R₂ respectively. The relation between moment of inertia of each disc about an axis passing through its centre and perpendicular to its plane and its thickness is ______.

Options

• `I_1t_2^2=I_2t_1^2`

• `I_1t_1=I_2t_2`

• `I_1t_2=I_2t_1`

• `I_1t_1^2=I_2t_2^2`

Answer 1

Two discs having moment of inertia I₁ and I₂ are made from same material have same mass. Their thickness and radii are t₁, t_2, and R₁, R₂ respectively. The relation between moment of inertia of each disc about an axis passing through its centre and perpendicular to its plane and its thickness is `underline(I_1t_1=I_2t_2)`.

Explanation:

`I_1=("mR"_1^2)/2`               `m_1=piR_1^2t_1`

`I_2=("mR"_2^2)/2`               `m_2=piR_2^2t_2`

`I_1/I_2=R_1^2/R_2^2=t_2/t_1`        m1 = m2     `therefore R_1^2t_1=R_2^2t_2`

`thereforeI_1t_1=I_2t_2`