Two circular discs have masses in the ratio 1 : 2 and radii in the rat...
Moment of inertia of a disc about its diameter:
Moment of inertia of a disc about its centre:
Calculation:Two circular discs have masses in the ratio 1: 2 and radii in the ratio 2: 1. The ratio of their moment of inertia about the diameter is
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Two circular discs have masses in the ratio 1 : 2 and radii in the rat...
Given:
- Mass ratio: 1 : 2
- Radius ratio: 2 : 1
To find:
The ratio of the moment of inertia about the diameter
Solution:
1. Moment of inertia:
The moment of inertia of a circular disc about an axis perpendicular to its plane and passing through its center is given by the formula:
I = (1/4) * m * r^2
Where:
- I is the moment of inertia
- m is the mass of the disc
- r is the radius of the disc
2. Calculation:
Let's assume the masses of the two discs as m1 and m2, and the radii as r1 and r2, respectively.
Given that the mass ratio is 1:2, we can write:
m1 : m2 = 1 : 2
Given that the radius ratio is 2:1, we can write:
r1 : r2 = 2 : 1
We can assume m1 = x, m2 = 2x, r1 = 2y, and r2 = y.
2.1 Moment of inertia of the first disc (I1):
Using the formula for moment of inertia, we can calculate the moment of inertia of the first disc as:
I1 = (1/4) * m1 * r1^2
= (1/4) * x * (2y)^2
= (1/4) * x * 4y^2
= x * y^2
2.2 Moment of inertia of the second disc (I2):
Using the formula for moment of inertia, we can calculate the moment of inertia of the second disc as:
I2 = (1/4) * m2 * r2^2
= (1/4) * 2x * y^2
= x * y^2
3. Ratio of the moment of inertia:
To find the ratio of the moment of inertia, we can divide I1 by I2:
I1 / I2 = (x * y^2) / (x * y^2)
= 1
Therefore, the ratio of the moment of inertia about the diameter is 1:1.
4. Answer:
Option (a) 1:1 is the correct ratio of the moment of inertia about the diameter.
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