Question
Four holes of radius 5 ~cm are cut from a thin square plate of 20 ~cm and mass 1 ~kg . The moment of inertia of the remaining portion about Z-axis is
BITSAT
Physics
Rotational Motion
2022
BITSAT 2022
BITSAT Physics Question (2022) — Solution
Options
- A. 15 ~kg - m ^2
- B. 0.37 ~kg - m ^2
- C. 0.0017 ~kg - m ^2
- D. 0.08 ~kg - m ^2
Answer
C. 0.0017 ~kg - m ^2
Step-by-step solution
Area mass density, = M 16 R^2 ( Area =4 R 4 R=16 R^2 ) Mass of each hole m_1= R^2= M 16 R^2 R^2= M 16 Distance between centre of plate and centre of hole x= (2 R)^2+(2 R)^2 2 = 2 2 R 2 . Moment of inertia of one hole at about Z-axis I_1= 1 2 m_1 R^2+m_1 x^2= 5 32 M R^2 Moment of inertia of whole plate about Z-axis, I= M(4 R)^2 6 = 8 3 M R^2 Required moment of Inertia I_0=I-4 I_1,= [ 8 3 -4 ( 5 32 ) ] M R^2= [ 8 3 - 5 8 ] M R^2 Given, R=5 ~cm and M=1 ~kg So, I_0= [ 8 3 - 5 8 ] 1 25 10^ -4 =0.0017 ~kg - m ^2
Related: Physics — Rotational Motion · All PYQ Banks