03. Moment of Inertia, Radius of Gyration
Rotational Motion

150139 A circular disc ' \(X\) ' of radius ' \(R\) ' made from iron plate of thickness ' \(t\) ' has moment of inertia ' \(I_{x}\) ' about an axis passing through the centre of disc and perpendicular to its plane. Another disc ' \(Y\) ' of radius ' \(3 R\) ' made from an iron plate of thickness \(\left(\frac{t}{3}\right)\) has moment of inertia ' \(I_{y}\) ', about the axis same as that of disc \(X\). The relation between \(I_{x}\) and \(I_{y}\) is

1 \(I_{y}=9 I_{x}\)
2 \(I_{y}=I_{x}\)
3 \(\mathrm{I}_{\mathrm{y}}=3 \mathrm{I}_{\mathrm{x}}\)
4 \(I_{y}=27 I_{x}\)
Rotational Motion

150140 Two rings of radii \(R\) and \(n R\) made from the same wire have the ratio of moments of inertia about an axis passing through their centre and perpendicular to the plane of the rings is \(1: 8\). The value of \(\mathbf{n}\) is

1 \(2 \sqrt{2}\)
2 2
3 4
4 \(\frac{1}{2}\)
Rotational Motion

150141 The torque necessary to produce an angular acceleration of 25 rad. \(\mathrm{s}^{-2}\) in a flywheel of mass \(50 \mathrm{~kg}\) and radius of gyration \(50 \mathrm{~cm}\) about its axis is

1 312.5 dyne. \(\mathrm{cm}\)
2 \(31.25 \mathrm{~N} . \mathrm{m}\)
3 31.25 dyne. \(\mathrm{cm}\)
4 \(312.5 \mathrm{~N} . \mathrm{m}\)
Rotational Motion

150142 The moment of inertia of a slab about a perpendicular axis passing through in centre is
\(M\left(\frac{\mathbf{a}^{2}+\mathbf{b}^{2}}{12}\right)\). The value of radius of Gyration,
\(K\) is

1 \(\frac{\left(a^{2}+b^{2}\right)^{1 / 2}}{2 \sqrt{3}}\)
2 \(\frac{a^{2}+b^{2}}{12}\)
3 \(\frac{\sqrt{a+b}}{5}\)
4 \(\frac{2}{5} \sqrt{a^{2}+b^{2}}\)
Rotational Motion

150139 A circular disc ' \(X\) ' of radius ' \(R\) ' made from iron plate of thickness ' \(t\) ' has moment of inertia ' \(I_{x}\) ' about an axis passing through the centre of disc and perpendicular to its plane. Another disc ' \(Y\) ' of radius ' \(3 R\) ' made from an iron plate of thickness \(\left(\frac{t}{3}\right)\) has moment of inertia ' \(I_{y}\) ', about the axis same as that of disc \(X\). The relation between \(I_{x}\) and \(I_{y}\) is

1 \(I_{y}=9 I_{x}\)
2 \(I_{y}=I_{x}\)
3 \(\mathrm{I}_{\mathrm{y}}=3 \mathrm{I}_{\mathrm{x}}\)
4 \(I_{y}=27 I_{x}\)
Rotational Motion

150140 Two rings of radii \(R\) and \(n R\) made from the same wire have the ratio of moments of inertia about an axis passing through their centre and perpendicular to the plane of the rings is \(1: 8\). The value of \(\mathbf{n}\) is

1 \(2 \sqrt{2}\)
2 2
3 4
4 \(\frac{1}{2}\)
Rotational Motion

150141 The torque necessary to produce an angular acceleration of 25 rad. \(\mathrm{s}^{-2}\) in a flywheel of mass \(50 \mathrm{~kg}\) and radius of gyration \(50 \mathrm{~cm}\) about its axis is

1 312.5 dyne. \(\mathrm{cm}\)
2 \(31.25 \mathrm{~N} . \mathrm{m}\)
3 31.25 dyne. \(\mathrm{cm}\)
4 \(312.5 \mathrm{~N} . \mathrm{m}\)
Rotational Motion

150142 The moment of inertia of a slab about a perpendicular axis passing through in centre is
\(M\left(\frac{\mathbf{a}^{2}+\mathbf{b}^{2}}{12}\right)\). The value of radius of Gyration,
\(K\) is

1 \(\frac{\left(a^{2}+b^{2}\right)^{1 / 2}}{2 \sqrt{3}}\)
2 \(\frac{a^{2}+b^{2}}{12}\)
3 \(\frac{\sqrt{a+b}}{5}\)
4 \(\frac{2}{5} \sqrt{a^{2}+b^{2}}\)
Rotational Motion

150139 A circular disc ' \(X\) ' of radius ' \(R\) ' made from iron plate of thickness ' \(t\) ' has moment of inertia ' \(I_{x}\) ' about an axis passing through the centre of disc and perpendicular to its plane. Another disc ' \(Y\) ' of radius ' \(3 R\) ' made from an iron plate of thickness \(\left(\frac{t}{3}\right)\) has moment of inertia ' \(I_{y}\) ', about the axis same as that of disc \(X\). The relation between \(I_{x}\) and \(I_{y}\) is

1 \(I_{y}=9 I_{x}\)
2 \(I_{y}=I_{x}\)
3 \(\mathrm{I}_{\mathrm{y}}=3 \mathrm{I}_{\mathrm{x}}\)
4 \(I_{y}=27 I_{x}\)
Rotational Motion

150140 Two rings of radii \(R\) and \(n R\) made from the same wire have the ratio of moments of inertia about an axis passing through their centre and perpendicular to the plane of the rings is \(1: 8\). The value of \(\mathbf{n}\) is

1 \(2 \sqrt{2}\)
2 2
3 4
4 \(\frac{1}{2}\)
Rotational Motion

150141 The torque necessary to produce an angular acceleration of 25 rad. \(\mathrm{s}^{-2}\) in a flywheel of mass \(50 \mathrm{~kg}\) and radius of gyration \(50 \mathrm{~cm}\) about its axis is

1 312.5 dyne. \(\mathrm{cm}\)
2 \(31.25 \mathrm{~N} . \mathrm{m}\)
3 31.25 dyne. \(\mathrm{cm}\)
4 \(312.5 \mathrm{~N} . \mathrm{m}\)
Rotational Motion

150142 The moment of inertia of a slab about a perpendicular axis passing through in centre is
\(M\left(\frac{\mathbf{a}^{2}+\mathbf{b}^{2}}{12}\right)\). The value of radius of Gyration,
\(K\) is

1 \(\frac{\left(a^{2}+b^{2}\right)^{1 / 2}}{2 \sqrt{3}}\)
2 \(\frac{a^{2}+b^{2}}{12}\)
3 \(\frac{\sqrt{a+b}}{5}\)
4 \(\frac{2}{5} \sqrt{a^{2}+b^{2}}\)
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Rotational Motion

150139 A circular disc ' \(X\) ' of radius ' \(R\) ' made from iron plate of thickness ' \(t\) ' has moment of inertia ' \(I_{x}\) ' about an axis passing through the centre of disc and perpendicular to its plane. Another disc ' \(Y\) ' of radius ' \(3 R\) ' made from an iron plate of thickness \(\left(\frac{t}{3}\right)\) has moment of inertia ' \(I_{y}\) ', about the axis same as that of disc \(X\). The relation between \(I_{x}\) and \(I_{y}\) is

1 \(I_{y}=9 I_{x}\)
2 \(I_{y}=I_{x}\)
3 \(\mathrm{I}_{\mathrm{y}}=3 \mathrm{I}_{\mathrm{x}}\)
4 \(I_{y}=27 I_{x}\)
Rotational Motion

150140 Two rings of radii \(R\) and \(n R\) made from the same wire have the ratio of moments of inertia about an axis passing through their centre and perpendicular to the plane of the rings is \(1: 8\). The value of \(\mathbf{n}\) is

1 \(2 \sqrt{2}\)
2 2
3 4
4 \(\frac{1}{2}\)
Rotational Motion

150141 The torque necessary to produce an angular acceleration of 25 rad. \(\mathrm{s}^{-2}\) in a flywheel of mass \(50 \mathrm{~kg}\) and radius of gyration \(50 \mathrm{~cm}\) about its axis is

1 312.5 dyne. \(\mathrm{cm}\)
2 \(31.25 \mathrm{~N} . \mathrm{m}\)
3 31.25 dyne. \(\mathrm{cm}\)
4 \(312.5 \mathrm{~N} . \mathrm{m}\)
Rotational Motion

150142 The moment of inertia of a slab about a perpendicular axis passing through in centre is
\(M\left(\frac{\mathbf{a}^{2}+\mathbf{b}^{2}}{12}\right)\). The value of radius of Gyration,
\(K\) is

1 \(\frac{\left(a^{2}+b^{2}\right)^{1 / 2}}{2 \sqrt{3}}\)
2 \(\frac{a^{2}+b^{2}}{12}\)
3 \(\frac{\sqrt{a+b}}{5}\)
4 \(\frac{2}{5} \sqrt{a^{2}+b^{2}}\)