03. Moment of Inertia, Radius of Gyration
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Rotational Motion

150126 Three point masses, each of mass ' \(m\) ' are placed at the corners of an equilateral triangle of side ' \(l\) '. The moment of inertia of the system about an axis along any one side of the triangle is

1 \(\mathrm{m} l^{2}\)
2 \(\frac{1}{3} \mathrm{~m} l^{2}\)
3 \(\frac{3}{2} \mathrm{~m} l^{2}\)
4 \(\frac{3}{4} \mathrm{~m} l^{2}\)
MHT-CET 2020
Rotational Motion

150127 Two discs having moment of inertia \(I_{1}\) and \(I_{2}\) are made from same material have same mass. Their thickness and radii are \(t_{1}, t_{2}\) and \(R_{1}, R_{2}\) 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

1 \(\mathrm{I}_{1} \mathrm{t}_{2}^{2}=\mathrm{I}_{2} \mathrm{t}_{1}^{2}\)
2 \(\mathrm{I}_{1} \mathrm{t}_{1}=\mathrm{I}_{2} \mathrm{t}_{2}\)
3 \(\mathrm{I}_{1} \mathrm{t}_{2}=\mathrm{I}_{2} \mathrm{t}_{1}\)
4 \(\mathrm{I}_{1} \mathrm{t}_{1}^{2}=\mathrm{I}_{2} \mathrm{t}_{2}^{2}\)
MHT-CET 2020
Rotational Motion

150128 Two circular rings ' \(A\) ' and ' \(B\) ' of radii ' \(n R\) ' and ' \(R\) ' are made from the same wire. The moment of inertia of ' \(A\) ' about an axis passing through the centre and perpendicular to the plane of ' \(A\) ' is 64 times that of the ring ' \(B\) '. The value of ' \(n\) ' is

1 3
2 4
3 8
4 6
MHT-CET 2020
Rotational Motion

150129 Four particles each of mass ' \(M\) ' are placed at corners of a square of side ' \(L\) '. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

1 \(\frac{\mathrm{L}}{\sqrt{2}}\)
2 \(\frac{\mathrm{L}}{\sqrt{8}}\)
3 \(\frac{\mathrm{L}}{\sqrt{5}}\)
4 \(\frac{\mathrm{L}}{\sqrt{3}}\)
MHT-CET 2020
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Rotational Motion

150126 Three point masses, each of mass ' \(m\) ' are placed at the corners of an equilateral triangle of side ' \(l\) '. The moment of inertia of the system about an axis along any one side of the triangle is

1 \(\mathrm{m} l^{2}\)
2 \(\frac{1}{3} \mathrm{~m} l^{2}\)
3 \(\frac{3}{2} \mathrm{~m} l^{2}\)
4 \(\frac{3}{4} \mathrm{~m} l^{2}\)
MHT-CET 2020
Rotational Motion

150127 Two discs having moment of inertia \(I_{1}\) and \(I_{2}\) are made from same material have same mass. Their thickness and radii are \(t_{1}, t_{2}\) and \(R_{1}, R_{2}\) 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

1 \(\mathrm{I}_{1} \mathrm{t}_{2}^{2}=\mathrm{I}_{2} \mathrm{t}_{1}^{2}\)
2 \(\mathrm{I}_{1} \mathrm{t}_{1}=\mathrm{I}_{2} \mathrm{t}_{2}\)
3 \(\mathrm{I}_{1} \mathrm{t}_{2}=\mathrm{I}_{2} \mathrm{t}_{1}\)
4 \(\mathrm{I}_{1} \mathrm{t}_{1}^{2}=\mathrm{I}_{2} \mathrm{t}_{2}^{2}\)
MHT-CET 2020
Rotational Motion

150128 Two circular rings ' \(A\) ' and ' \(B\) ' of radii ' \(n R\) ' and ' \(R\) ' are made from the same wire. The moment of inertia of ' \(A\) ' about an axis passing through the centre and perpendicular to the plane of ' \(A\) ' is 64 times that of the ring ' \(B\) '. The value of ' \(n\) ' is

1 3
2 4
3 8
4 6
MHT-CET 2020
Rotational Motion

150129 Four particles each of mass ' \(M\) ' are placed at corners of a square of side ' \(L\) '. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

1 \(\frac{\mathrm{L}}{\sqrt{2}}\)
2 \(\frac{\mathrm{L}}{\sqrt{8}}\)
3 \(\frac{\mathrm{L}}{\sqrt{5}}\)
4 \(\frac{\mathrm{L}}{\sqrt{3}}\)
MHT-CET 2020
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Rotational Motion

150126 Three point masses, each of mass ' \(m\) ' are placed at the corners of an equilateral triangle of side ' \(l\) '. The moment of inertia of the system about an axis along any one side of the triangle is

1 \(\mathrm{m} l^{2}\)
2 \(\frac{1}{3} \mathrm{~m} l^{2}\)
3 \(\frac{3}{2} \mathrm{~m} l^{2}\)
4 \(\frac{3}{4} \mathrm{~m} l^{2}\)
MHT-CET 2020
Rotational Motion

150127 Two discs having moment of inertia \(I_{1}\) and \(I_{2}\) are made from same material have same mass. Their thickness and radii are \(t_{1}, t_{2}\) and \(R_{1}, R_{2}\) 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

1 \(\mathrm{I}_{1} \mathrm{t}_{2}^{2}=\mathrm{I}_{2} \mathrm{t}_{1}^{2}\)
2 \(\mathrm{I}_{1} \mathrm{t}_{1}=\mathrm{I}_{2} \mathrm{t}_{2}\)
3 \(\mathrm{I}_{1} \mathrm{t}_{2}=\mathrm{I}_{2} \mathrm{t}_{1}\)
4 \(\mathrm{I}_{1} \mathrm{t}_{1}^{2}=\mathrm{I}_{2} \mathrm{t}_{2}^{2}\)
MHT-CET 2020
Rotational Motion

150128 Two circular rings ' \(A\) ' and ' \(B\) ' of radii ' \(n R\) ' and ' \(R\) ' are made from the same wire. The moment of inertia of ' \(A\) ' about an axis passing through the centre and perpendicular to the plane of ' \(A\) ' is 64 times that of the ring ' \(B\) '. The value of ' \(n\) ' is

1 3
2 4
3 8
4 6
MHT-CET 2020
Rotational Motion

150129 Four particles each of mass ' \(M\) ' are placed at corners of a square of side ' \(L\) '. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

1 \(\frac{\mathrm{L}}{\sqrt{2}}\)
2 \(\frac{\mathrm{L}}{\sqrt{8}}\)
3 \(\frac{\mathrm{L}}{\sqrt{5}}\)
4 \(\frac{\mathrm{L}}{\sqrt{3}}\)
MHT-CET 2020
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Rotational Motion

150126 Three point masses, each of mass ' \(m\) ' are placed at the corners of an equilateral triangle of side ' \(l\) '. The moment of inertia of the system about an axis along any one side of the triangle is

1 \(\mathrm{m} l^{2}\)
2 \(\frac{1}{3} \mathrm{~m} l^{2}\)
3 \(\frac{3}{2} \mathrm{~m} l^{2}\)
4 \(\frac{3}{4} \mathrm{~m} l^{2}\)
MHT-CET 2020
Rotational Motion

150127 Two discs having moment of inertia \(I_{1}\) and \(I_{2}\) are made from same material have same mass. Their thickness and radii are \(t_{1}, t_{2}\) and \(R_{1}, R_{2}\) 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

1 \(\mathrm{I}_{1} \mathrm{t}_{2}^{2}=\mathrm{I}_{2} \mathrm{t}_{1}^{2}\)
2 \(\mathrm{I}_{1} \mathrm{t}_{1}=\mathrm{I}_{2} \mathrm{t}_{2}\)
3 \(\mathrm{I}_{1} \mathrm{t}_{2}=\mathrm{I}_{2} \mathrm{t}_{1}\)
4 \(\mathrm{I}_{1} \mathrm{t}_{1}^{2}=\mathrm{I}_{2} \mathrm{t}_{2}^{2}\)
MHT-CET 2020
Rotational Motion

150128 Two circular rings ' \(A\) ' and ' \(B\) ' of radii ' \(n R\) ' and ' \(R\) ' are made from the same wire. The moment of inertia of ' \(A\) ' about an axis passing through the centre and perpendicular to the plane of ' \(A\) ' is 64 times that of the ring ' \(B\) '. The value of ' \(n\) ' is

1 3
2 4
3 8
4 6
MHT-CET 2020
Rotational Motion

150129 Four particles each of mass ' \(M\) ' are placed at corners of a square of side ' \(L\) '. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

1 \(\frac{\mathrm{L}}{\sqrt{2}}\)
2 \(\frac{\mathrm{L}}{\sqrt{8}}\)
3 \(\frac{\mathrm{L}}{\sqrt{5}}\)
4 \(\frac{\mathrm{L}}{\sqrt{3}}\)
MHT-CET 2020
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