03. Moment of Inertia, Radius of Gyration
Rotational Motion

150170 A disc of moment of inertia \(2 \mathrm{~kg}-\mathrm{m}^{2}\) revolving with \(8 \mathrm{rad} / \mathrm{s}\) is placed on another side of moment of inertia \(4 \mathrm{~kg}-\mathrm{m}^{2}\) revolving \(4 \mathrm{rad} / \mathrm{s}\). What is the angular frequency of composite disc?

1 \(4 \mathrm{rad} / \mathrm{s}\)
2 \(\frac{3}{16} \mathrm{rad} / \mathrm{s}\)
3 \(\frac{16}{3} \mathrm{rad} / \mathrm{s}\)
4 \(\frac{16}{5} \mathrm{rad} / \mathrm{s}\)
Rotational Motion

150171 Two blocks of masses \(10 \mathrm{~kg}\) and \(4 \mathrm{~kg}\) are connected by a spring of negligible mass and placed on a horizontal frictionless surface. An impulse gives a velocity of \(14 \mathrm{~m} / \mathrm{s}\) to the heavier block in the direction of the lighter block. What is the velocity of the centre of mass?

1 \(5 \mathrm{~m} / \mathrm{s}\)
2 \(10 \mathrm{~m} / \mathrm{s}\)
3 \(20 \mathrm{~m} / \mathrm{s}\)
4 \(30 \mathrm{~m} / \mathrm{s}\)
Rotational Motion

150172 The ratio of the radii of gyration of a circular disc and a circular ring of the same radius and same mass about a tangential axis perpendicular to plane of disc or ring is

1 \(\sqrt{3}: 2\)
2 \(2: 3\)
3 \(1: 2\)
4 \(\sqrt{5}: \sqrt{6}\)
Rotational Motion

150174 The moment of inertia of a uniform horizontal solid cylinder of mass \(M\) about an axis passing through its edge and perpendicular to the axis of the cylinder, when its length is 6 times its radius \(R\), is

1 \(\frac{49 \mathrm{MR}^{2}}{4}\)
2 \(\frac{39 \mathrm{MR}^{2}}{4}\)
3 \(\frac{36 \mathrm{MR}^{2}}{11}\)
4 \(\frac{3 \mathrm{MR}^{2}}{2}\)
Rotational Motion

150170 A disc of moment of inertia \(2 \mathrm{~kg}-\mathrm{m}^{2}\) revolving with \(8 \mathrm{rad} / \mathrm{s}\) is placed on another side of moment of inertia \(4 \mathrm{~kg}-\mathrm{m}^{2}\) revolving \(4 \mathrm{rad} / \mathrm{s}\). What is the angular frequency of composite disc?

1 \(4 \mathrm{rad} / \mathrm{s}\)
2 \(\frac{3}{16} \mathrm{rad} / \mathrm{s}\)
3 \(\frac{16}{3} \mathrm{rad} / \mathrm{s}\)
4 \(\frac{16}{5} \mathrm{rad} / \mathrm{s}\)
Rotational Motion

150171 Two blocks of masses \(10 \mathrm{~kg}\) and \(4 \mathrm{~kg}\) are connected by a spring of negligible mass and placed on a horizontal frictionless surface. An impulse gives a velocity of \(14 \mathrm{~m} / \mathrm{s}\) to the heavier block in the direction of the lighter block. What is the velocity of the centre of mass?

1 \(5 \mathrm{~m} / \mathrm{s}\)
2 \(10 \mathrm{~m} / \mathrm{s}\)
3 \(20 \mathrm{~m} / \mathrm{s}\)
4 \(30 \mathrm{~m} / \mathrm{s}\)
Rotational Motion

150172 The ratio of the radii of gyration of a circular disc and a circular ring of the same radius and same mass about a tangential axis perpendicular to plane of disc or ring is

1 \(\sqrt{3}: 2\)
2 \(2: 3\)
3 \(1: 2\)
4 \(\sqrt{5}: \sqrt{6}\)
Rotational Motion

150174 The moment of inertia of a uniform horizontal solid cylinder of mass \(M\) about an axis passing through its edge and perpendicular to the axis of the cylinder, when its length is 6 times its radius \(R\), is

1 \(\frac{49 \mathrm{MR}^{2}}{4}\)
2 \(\frac{39 \mathrm{MR}^{2}}{4}\)
3 \(\frac{36 \mathrm{MR}^{2}}{11}\)
4 \(\frac{3 \mathrm{MR}^{2}}{2}\)
Rotational Motion

150170 A disc of moment of inertia \(2 \mathrm{~kg}-\mathrm{m}^{2}\) revolving with \(8 \mathrm{rad} / \mathrm{s}\) is placed on another side of moment of inertia \(4 \mathrm{~kg}-\mathrm{m}^{2}\) revolving \(4 \mathrm{rad} / \mathrm{s}\). What is the angular frequency of composite disc?

1 \(4 \mathrm{rad} / \mathrm{s}\)
2 \(\frac{3}{16} \mathrm{rad} / \mathrm{s}\)
3 \(\frac{16}{3} \mathrm{rad} / \mathrm{s}\)
4 \(\frac{16}{5} \mathrm{rad} / \mathrm{s}\)
Rotational Motion

150171 Two blocks of masses \(10 \mathrm{~kg}\) and \(4 \mathrm{~kg}\) are connected by a spring of negligible mass and placed on a horizontal frictionless surface. An impulse gives a velocity of \(14 \mathrm{~m} / \mathrm{s}\) to the heavier block in the direction of the lighter block. What is the velocity of the centre of mass?

1 \(5 \mathrm{~m} / \mathrm{s}\)
2 \(10 \mathrm{~m} / \mathrm{s}\)
3 \(20 \mathrm{~m} / \mathrm{s}\)
4 \(30 \mathrm{~m} / \mathrm{s}\)
Rotational Motion

150172 The ratio of the radii of gyration of a circular disc and a circular ring of the same radius and same mass about a tangential axis perpendicular to plane of disc or ring is

1 \(\sqrt{3}: 2\)
2 \(2: 3\)
3 \(1: 2\)
4 \(\sqrt{5}: \sqrt{6}\)
Rotational Motion

150174 The moment of inertia of a uniform horizontal solid cylinder of mass \(M\) about an axis passing through its edge and perpendicular to the axis of the cylinder, when its length is 6 times its radius \(R\), is

1 \(\frac{49 \mathrm{MR}^{2}}{4}\)
2 \(\frac{39 \mathrm{MR}^{2}}{4}\)
3 \(\frac{36 \mathrm{MR}^{2}}{11}\)
4 \(\frac{3 \mathrm{MR}^{2}}{2}\)
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Rotational Motion

150170 A disc of moment of inertia \(2 \mathrm{~kg}-\mathrm{m}^{2}\) revolving with \(8 \mathrm{rad} / \mathrm{s}\) is placed on another side of moment of inertia \(4 \mathrm{~kg}-\mathrm{m}^{2}\) revolving \(4 \mathrm{rad} / \mathrm{s}\). What is the angular frequency of composite disc?

1 \(4 \mathrm{rad} / \mathrm{s}\)
2 \(\frac{3}{16} \mathrm{rad} / \mathrm{s}\)
3 \(\frac{16}{3} \mathrm{rad} / \mathrm{s}\)
4 \(\frac{16}{5} \mathrm{rad} / \mathrm{s}\)
Rotational Motion

150171 Two blocks of masses \(10 \mathrm{~kg}\) and \(4 \mathrm{~kg}\) are connected by a spring of negligible mass and placed on a horizontal frictionless surface. An impulse gives a velocity of \(14 \mathrm{~m} / \mathrm{s}\) to the heavier block in the direction of the lighter block. What is the velocity of the centre of mass?

1 \(5 \mathrm{~m} / \mathrm{s}\)
2 \(10 \mathrm{~m} / \mathrm{s}\)
3 \(20 \mathrm{~m} / \mathrm{s}\)
4 \(30 \mathrm{~m} / \mathrm{s}\)
Rotational Motion

150172 The ratio of the radii of gyration of a circular disc and a circular ring of the same radius and same mass about a tangential axis perpendicular to plane of disc or ring is

1 \(\sqrt{3}: 2\)
2 \(2: 3\)
3 \(1: 2\)
4 \(\sqrt{5}: \sqrt{6}\)
Rotational Motion

150174 The moment of inertia of a uniform horizontal solid cylinder of mass \(M\) about an axis passing through its edge and perpendicular to the axis of the cylinder, when its length is 6 times its radius \(R\), is

1 \(\frac{49 \mathrm{MR}^{2}}{4}\)
2 \(\frac{39 \mathrm{MR}^{2}}{4}\)
3 \(\frac{36 \mathrm{MR}^{2}}{11}\)
4 \(\frac{3 \mathrm{MR}^{2}}{2}\)