Question

A thin uniform rectangular plate of mass 2 kg is placed in X-Y plane as shown in figure. The moment of inertial about x-axis is Ix = 0.2 kg m² and the moment of inertia about y-axis is Iy = 0.3 kg m². The radius of gyration of the plate about the axis passing through O and perpendicular to the plane of the plate is

• A. 50 cm
• B. 5 cm
• C. 38.7 cm
• D. 31.6 cm

Answer 1

The Correct Option is A

The radius of gyration \( k \) of the plate about an axis perpendicular to the plane is given by: \[ k = \sqrt{\frac{I_x + I_y}{m}} \] Where:
\( I_x = 0.2 \, \text{kg} \, \text{m}^2 \) is the moment of inertia about the x-axis,
\( I_y = 0.3 \, \text{kg} \, \text{m}^2 \) is the moment of inertia about the y-axis,
\( m = 2 \, \text{kg} \) is the mass of the plate. Substituting the values: \[ k = \sqrt{\frac{0.2 + 0.3}{2}} = \sqrt{\frac{0.5}{2}} = \sqrt{0.25} = 0.5 \, \text{m} = 50 \, \text{cm} \]

The correct answer is (A) : 50 cm.