ROTATIONAL INERTIA OF SOLID BODIES, ROTATIONAL DYNAMICS
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Rotational Motion

269526 Two point size bodies of masses\(2 \mathrm{~kg}, 3 \mathrm{~kg}\) are fixed at two ends of a light rod of length \(1 \mathrm{~m}\). The moment of inertia of two bodies about an axis perpendicular to the length of rod and passing through centre of mass of two bodies is

1 \(0.6 \mathrm{kgm}^{2} \)
2 \(0.8 \mathrm{kgm}^{2}\)
3 \(1 \mathrm{kgm}^{2} \)
4 \(1.2 \mathrm{kgm}^{2}\)
Rotational Motion

269509 A thin rod of mass\(M\) and length \(L\) is bent into \(a\) circular ring. The expression for moment of inertia of ring about an axis passing through its diameter is

1 \(\frac{\mathrm{ML}^{2}}{2 \pi^{2}}\)
2 \(\frac{M L^{2}}{4 \pi^{2}}\)
3 \(\frac{\mathrm{ML}^{2}}{8 \pi^{2}}\)
4 \(\frac{\mathrm{ML}^{2}}{\pi^{2}}\)
Rotational Motion

269510 Two identical circular plates each of mass 0.1\(\mathrm{kg}\) and radius \(10 \mathrm{~cm}\) are joined side by side as shown in the figure. Their moment of inertia about an axis passing through their common tangent is

1 \(1.25 \times 10^{-3} \mathrm{kgm}^{2}\)
2 \(2.5 \times 10^{-3} \mathrm{kgm}^{2}\)
3 \(1.25 \times 10^{-2} \mathrm{kgm}^{2}\)
4 \(2.5 \times 10^{-2} \mathrm{kgm}^{2}\)
Rotational Motion

269511 A wheel starting from rest is uniformly accelerated with\(\alpha=4 \mathrm{rad} / \mathrm{s}^{2}\) for \(\mathbf{1 0}\) seconds. It is then allowed to rotate uniformly for the next two seconds and is finally brought to rest in the next 10 seconds. Find the total angle rotated by the wheel.

1 \(200 \mathrm{rad}\)
2 \(400 \mathrm{rad}\)
3 \(300 \mathrm{rad}\)
4 \(480 \mathrm{rad}\)
Rotational Motion

269512 Two spheres each of mass\(M\) and radius \(R / 2\) are connected with a massless rod of length \(2 R\) as shown in the figure. The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod is

1 \(\frac{21}{5} M R^{2}\)
2 \(\frac{2}{5} M R^{2}\)
3 \(\frac{5}{2} M R^{2}\)
4 \(\frac{5}{21} M R^{2}\)
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Rotational Motion

269526 Two point size bodies of masses\(2 \mathrm{~kg}, 3 \mathrm{~kg}\) are fixed at two ends of a light rod of length \(1 \mathrm{~m}\). The moment of inertia of two bodies about an axis perpendicular to the length of rod and passing through centre of mass of two bodies is

1 \(0.6 \mathrm{kgm}^{2} \)
2 \(0.8 \mathrm{kgm}^{2}\)
3 \(1 \mathrm{kgm}^{2} \)
4 \(1.2 \mathrm{kgm}^{2}\)
Rotational Motion

269509 A thin rod of mass\(M\) and length \(L\) is bent into \(a\) circular ring. The expression for moment of inertia of ring about an axis passing through its diameter is

1 \(\frac{\mathrm{ML}^{2}}{2 \pi^{2}}\)
2 \(\frac{M L^{2}}{4 \pi^{2}}\)
3 \(\frac{\mathrm{ML}^{2}}{8 \pi^{2}}\)
4 \(\frac{\mathrm{ML}^{2}}{\pi^{2}}\)
Rotational Motion

269510 Two identical circular plates each of mass 0.1\(\mathrm{kg}\) and radius \(10 \mathrm{~cm}\) are joined side by side as shown in the figure. Their moment of inertia about an axis passing through their common tangent is

1 \(1.25 \times 10^{-3} \mathrm{kgm}^{2}\)
2 \(2.5 \times 10^{-3} \mathrm{kgm}^{2}\)
3 \(1.25 \times 10^{-2} \mathrm{kgm}^{2}\)
4 \(2.5 \times 10^{-2} \mathrm{kgm}^{2}\)
Rotational Motion

269511 A wheel starting from rest is uniformly accelerated with\(\alpha=4 \mathrm{rad} / \mathrm{s}^{2}\) for \(\mathbf{1 0}\) seconds. It is then allowed to rotate uniformly for the next two seconds and is finally brought to rest in the next 10 seconds. Find the total angle rotated by the wheel.

1 \(200 \mathrm{rad}\)
2 \(400 \mathrm{rad}\)
3 \(300 \mathrm{rad}\)
4 \(480 \mathrm{rad}\)
Rotational Motion

269512 Two spheres each of mass\(M\) and radius \(R / 2\) are connected with a massless rod of length \(2 R\) as shown in the figure. The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod is

1 \(\frac{21}{5} M R^{2}\)
2 \(\frac{2}{5} M R^{2}\)
3 \(\frac{5}{2} M R^{2}\)
4 \(\frac{5}{21} M R^{2}\)
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Rotational Motion

269526 Two point size bodies of masses\(2 \mathrm{~kg}, 3 \mathrm{~kg}\) are fixed at two ends of a light rod of length \(1 \mathrm{~m}\). The moment of inertia of two bodies about an axis perpendicular to the length of rod and passing through centre of mass of two bodies is

1 \(0.6 \mathrm{kgm}^{2} \)
2 \(0.8 \mathrm{kgm}^{2}\)
3 \(1 \mathrm{kgm}^{2} \)
4 \(1.2 \mathrm{kgm}^{2}\)
Rotational Motion

269509 A thin rod of mass\(M\) and length \(L\) is bent into \(a\) circular ring. The expression for moment of inertia of ring about an axis passing through its diameter is

1 \(\frac{\mathrm{ML}^{2}}{2 \pi^{2}}\)
2 \(\frac{M L^{2}}{4 \pi^{2}}\)
3 \(\frac{\mathrm{ML}^{2}}{8 \pi^{2}}\)
4 \(\frac{\mathrm{ML}^{2}}{\pi^{2}}\)
Rotational Motion

269510 Two identical circular plates each of mass 0.1\(\mathrm{kg}\) and radius \(10 \mathrm{~cm}\) are joined side by side as shown in the figure. Their moment of inertia about an axis passing through their common tangent is

1 \(1.25 \times 10^{-3} \mathrm{kgm}^{2}\)
2 \(2.5 \times 10^{-3} \mathrm{kgm}^{2}\)
3 \(1.25 \times 10^{-2} \mathrm{kgm}^{2}\)
4 \(2.5 \times 10^{-2} \mathrm{kgm}^{2}\)
Rotational Motion

269511 A wheel starting from rest is uniformly accelerated with\(\alpha=4 \mathrm{rad} / \mathrm{s}^{2}\) for \(\mathbf{1 0}\) seconds. It is then allowed to rotate uniformly for the next two seconds and is finally brought to rest in the next 10 seconds. Find the total angle rotated by the wheel.

1 \(200 \mathrm{rad}\)
2 \(400 \mathrm{rad}\)
3 \(300 \mathrm{rad}\)
4 \(480 \mathrm{rad}\)
Rotational Motion

269512 Two spheres each of mass\(M\) and radius \(R / 2\) are connected with a massless rod of length \(2 R\) as shown in the figure. The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod is

1 \(\frac{21}{5} M R^{2}\)
2 \(\frac{2}{5} M R^{2}\)
3 \(\frac{5}{2} M R^{2}\)
4 \(\frac{5}{21} M R^{2}\)
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Rotational Motion

269526 Two point size bodies of masses\(2 \mathrm{~kg}, 3 \mathrm{~kg}\) are fixed at two ends of a light rod of length \(1 \mathrm{~m}\). The moment of inertia of two bodies about an axis perpendicular to the length of rod and passing through centre of mass of two bodies is

1 \(0.6 \mathrm{kgm}^{2} \)
2 \(0.8 \mathrm{kgm}^{2}\)
3 \(1 \mathrm{kgm}^{2} \)
4 \(1.2 \mathrm{kgm}^{2}\)
Rotational Motion

269509 A thin rod of mass\(M\) and length \(L\) is bent into \(a\) circular ring. The expression for moment of inertia of ring about an axis passing through its diameter is

1 \(\frac{\mathrm{ML}^{2}}{2 \pi^{2}}\)
2 \(\frac{M L^{2}}{4 \pi^{2}}\)
3 \(\frac{\mathrm{ML}^{2}}{8 \pi^{2}}\)
4 \(\frac{\mathrm{ML}^{2}}{\pi^{2}}\)
Rotational Motion

269510 Two identical circular plates each of mass 0.1\(\mathrm{kg}\) and radius \(10 \mathrm{~cm}\) are joined side by side as shown in the figure. Their moment of inertia about an axis passing through their common tangent is

1 \(1.25 \times 10^{-3} \mathrm{kgm}^{2}\)
2 \(2.5 \times 10^{-3} \mathrm{kgm}^{2}\)
3 \(1.25 \times 10^{-2} \mathrm{kgm}^{2}\)
4 \(2.5 \times 10^{-2} \mathrm{kgm}^{2}\)
Rotational Motion

269511 A wheel starting from rest is uniformly accelerated with\(\alpha=4 \mathrm{rad} / \mathrm{s}^{2}\) for \(\mathbf{1 0}\) seconds. It is then allowed to rotate uniformly for the next two seconds and is finally brought to rest in the next 10 seconds. Find the total angle rotated by the wheel.

1 \(200 \mathrm{rad}\)
2 \(400 \mathrm{rad}\)
3 \(300 \mathrm{rad}\)
4 \(480 \mathrm{rad}\)
Rotational Motion

269512 Two spheres each of mass\(M\) and radius \(R / 2\) are connected with a massless rod of length \(2 R\) as shown in the figure. The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod is

1 \(\frac{21}{5} M R^{2}\)
2 \(\frac{2}{5} M R^{2}\)
3 \(\frac{5}{2} M R^{2}\)
4 \(\frac{5}{21} M R^{2}\)
NEET DIGITAL LIBRARY
Rotational Motion

269526 Two point size bodies of masses\(2 \mathrm{~kg}, 3 \mathrm{~kg}\) are fixed at two ends of a light rod of length \(1 \mathrm{~m}\). The moment of inertia of two bodies about an axis perpendicular to the length of rod and passing through centre of mass of two bodies is

1 \(0.6 \mathrm{kgm}^{2} \)
2 \(0.8 \mathrm{kgm}^{2}\)
3 \(1 \mathrm{kgm}^{2} \)
4 \(1.2 \mathrm{kgm}^{2}\)
Rotational Motion

269509 A thin rod of mass\(M\) and length \(L\) is bent into \(a\) circular ring. The expression for moment of inertia of ring about an axis passing through its diameter is

1 \(\frac{\mathrm{ML}^{2}}{2 \pi^{2}}\)
2 \(\frac{M L^{2}}{4 \pi^{2}}\)
3 \(\frac{\mathrm{ML}^{2}}{8 \pi^{2}}\)
4 \(\frac{\mathrm{ML}^{2}}{\pi^{2}}\)
Rotational Motion

269510 Two identical circular plates each of mass 0.1\(\mathrm{kg}\) and radius \(10 \mathrm{~cm}\) are joined side by side as shown in the figure. Their moment of inertia about an axis passing through their common tangent is

1 \(1.25 \times 10^{-3} \mathrm{kgm}^{2}\)
2 \(2.5 \times 10^{-3} \mathrm{kgm}^{2}\)
3 \(1.25 \times 10^{-2} \mathrm{kgm}^{2}\)
4 \(2.5 \times 10^{-2} \mathrm{kgm}^{2}\)
Rotational Motion

269511 A wheel starting from rest is uniformly accelerated with\(\alpha=4 \mathrm{rad} / \mathrm{s}^{2}\) for \(\mathbf{1 0}\) seconds. It is then allowed to rotate uniformly for the next two seconds and is finally brought to rest in the next 10 seconds. Find the total angle rotated by the wheel.

1 \(200 \mathrm{rad}\)
2 \(400 \mathrm{rad}\)
3 \(300 \mathrm{rad}\)
4 \(480 \mathrm{rad}\)
Rotational Motion

269512 Two spheres each of mass\(M\) and radius \(R / 2\) are connected with a massless rod of length \(2 R\) as shown in the figure. The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod is

1 \(\frac{21}{5} M R^{2}\)
2 \(\frac{2}{5} M R^{2}\)
3 \(\frac{5}{2} M R^{2}\)
4 \(\frac{5}{21} M R^{2}\)