A solid cylinder of mass \(M\) and radius \(R\) rolls on a flat surface. Its moment of inertia about the line of contact is

• Correct answer
  A

  \(\left(\frac{3}{2}\right) M R^2\)
• B

  \(M R^2\)
• C

  \(\left(\frac{2}{3}\right) M R^2\)
• D

  \(2 M R^2\)

Solution

Moment of inertia of solid cylinder of radius \(R\) and mass \(M\) about its axis is given as \(I_{\mathrm{CM}}=\frac{1}{2} M R^2\) ...(i) Moment of inertia about contact line \(A B\) is given
According to parallel axes theorem, i.e. \(\quad I_{A B}=I_{\mathrm{CM}}+M R^2=\frac{1}{2} M R^2+M R^2=\frac{3}{2} M R^2\)

Hence, the correct answer is option: 'A'.