03. Moment of Inertia, Radius of Gyration
Rotational Motion

150116 From a uniform circular thin disc of mass 9M and radius \(R\), a small disc of radius \(\frac{R}{3}\) is removed. The centre of the small disc is at a distance \(\frac{2 R}{3}\) from the centre of original disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through the centre of the disc of radius \(R\) is

1 \(\frac{\mathrm{MR}^{2}}{2}\)
2 \(4 \mathrm{MR}^{2}\)
3 \(\mathrm{MR}^{2}\)
4 \(3 \mathrm{MR}^{2}\)
Rotational Motion

150117 A disc of mass \(10 \mathrm{~kg}\) and radius \(0.1 \mathrm{~m}\) is rotating at 120 r.p.m. A retarding torque brings it to rest in 10s. If the same torque is due to force applied tangentially on the rim of the disc then magnitude of force is

1 \(0.1 \pi \mathrm{N}\)
2 \(0.2 \pi \mathrm{N}\)
3 \(0.4 \pi \mathrm{N}\)
4 \(0.8 \pi \mathrm{N}\)
Rotational Motion

150118 A thin wire of length ' \(L\) ' and uniform linear mass density ' \(m\) ' is bent into a circular loop. The moment of inertia of this loop about the tangential axis and in the plane of the coil is

1 \(\frac{3 \mathrm{~mL}^{3}}{4 \pi^{2}}\)
2 \(\frac{3 \mathrm{~mL}^{3}}{8 \pi^{2}}\)
3 \(\frac{3 \mathrm{~mL}^{3}}{16 \pi^{2}}\)
4 \(\frac{3 \mathrm{~mL}^{3}}{2 \pi^{2}}\)
[МHT-CET 2020]
Rotational Motion

150119 A solid sphere has mass ' \(M\) ' and radius ' \(R\) '. Its moment of inertia about a parallel axis passing through a point at a distance \(\frac{R}{2}\) from its centre
is

1 \(\frac{13}{20} \mathrm{MR}^{2}\)
2 \(\frac{8}{11} \mathrm{MR}^{2}\)
3 \(\frac{11}{15} \mathrm{MR}^{2}\)
4 \(\frac{6}{10} \mathrm{MR}^{2}\)
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Rotational Motion

150116 From a uniform circular thin disc of mass 9M and radius \(R\), a small disc of radius \(\frac{R}{3}\) is removed. The centre of the small disc is at a distance \(\frac{2 R}{3}\) from the centre of original disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through the centre of the disc of radius \(R\) is

1 \(\frac{\mathrm{MR}^{2}}{2}\)
2 \(4 \mathrm{MR}^{2}\)
3 \(\mathrm{MR}^{2}\)
4 \(3 \mathrm{MR}^{2}\)
Rotational Motion

150117 A disc of mass \(10 \mathrm{~kg}\) and radius \(0.1 \mathrm{~m}\) is rotating at 120 r.p.m. A retarding torque brings it to rest in 10s. If the same torque is due to force applied tangentially on the rim of the disc then magnitude of force is

1 \(0.1 \pi \mathrm{N}\)
2 \(0.2 \pi \mathrm{N}\)
3 \(0.4 \pi \mathrm{N}\)
4 \(0.8 \pi \mathrm{N}\)
Rotational Motion

150118 A thin wire of length ' \(L\) ' and uniform linear mass density ' \(m\) ' is bent into a circular loop. The moment of inertia of this loop about the tangential axis and in the plane of the coil is

1 \(\frac{3 \mathrm{~mL}^{3}}{4 \pi^{2}}\)
2 \(\frac{3 \mathrm{~mL}^{3}}{8 \pi^{2}}\)
3 \(\frac{3 \mathrm{~mL}^{3}}{16 \pi^{2}}\)
4 \(\frac{3 \mathrm{~mL}^{3}}{2 \pi^{2}}\)
[МHT-CET 2020]
Rotational Motion

150119 A solid sphere has mass ' \(M\) ' and radius ' \(R\) '. Its moment of inertia about a parallel axis passing through a point at a distance \(\frac{R}{2}\) from its centre
is

1 \(\frac{13}{20} \mathrm{MR}^{2}\)
2 \(\frac{8}{11} \mathrm{MR}^{2}\)
3 \(\frac{11}{15} \mathrm{MR}^{2}\)
4 \(\frac{6}{10} \mathrm{MR}^{2}\)
Rotational Motion

150116 From a uniform circular thin disc of mass 9M and radius \(R\), a small disc of radius \(\frac{R}{3}\) is removed. The centre of the small disc is at a distance \(\frac{2 R}{3}\) from the centre of original disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through the centre of the disc of radius \(R\) is

1 \(\frac{\mathrm{MR}^{2}}{2}\)
2 \(4 \mathrm{MR}^{2}\)
3 \(\mathrm{MR}^{2}\)
4 \(3 \mathrm{MR}^{2}\)
Rotational Motion

150117 A disc of mass \(10 \mathrm{~kg}\) and radius \(0.1 \mathrm{~m}\) is rotating at 120 r.p.m. A retarding torque brings it to rest in 10s. If the same torque is due to force applied tangentially on the rim of the disc then magnitude of force is

1 \(0.1 \pi \mathrm{N}\)
2 \(0.2 \pi \mathrm{N}\)
3 \(0.4 \pi \mathrm{N}\)
4 \(0.8 \pi \mathrm{N}\)
Rotational Motion

150118 A thin wire of length ' \(L\) ' and uniform linear mass density ' \(m\) ' is bent into a circular loop. The moment of inertia of this loop about the tangential axis and in the plane of the coil is

1 \(\frac{3 \mathrm{~mL}^{3}}{4 \pi^{2}}\)
2 \(\frac{3 \mathrm{~mL}^{3}}{8 \pi^{2}}\)
3 \(\frac{3 \mathrm{~mL}^{3}}{16 \pi^{2}}\)
4 \(\frac{3 \mathrm{~mL}^{3}}{2 \pi^{2}}\)
[МHT-CET 2020]
Rotational Motion

150119 A solid sphere has mass ' \(M\) ' and radius ' \(R\) '. Its moment of inertia about a parallel axis passing through a point at a distance \(\frac{R}{2}\) from its centre
is

1 \(\frac{13}{20} \mathrm{MR}^{2}\)
2 \(\frac{8}{11} \mathrm{MR}^{2}\)
3 \(\frac{11}{15} \mathrm{MR}^{2}\)
4 \(\frac{6}{10} \mathrm{MR}^{2}\)
Rotational Motion

150116 From a uniform circular thin disc of mass 9M and radius \(R\), a small disc of radius \(\frac{R}{3}\) is removed. The centre of the small disc is at a distance \(\frac{2 R}{3}\) from the centre of original disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through the centre of the disc of radius \(R\) is

1 \(\frac{\mathrm{MR}^{2}}{2}\)
2 \(4 \mathrm{MR}^{2}\)
3 \(\mathrm{MR}^{2}\)
4 \(3 \mathrm{MR}^{2}\)
Rotational Motion

150117 A disc of mass \(10 \mathrm{~kg}\) and radius \(0.1 \mathrm{~m}\) is rotating at 120 r.p.m. A retarding torque brings it to rest in 10s. If the same torque is due to force applied tangentially on the rim of the disc then magnitude of force is

1 \(0.1 \pi \mathrm{N}\)
2 \(0.2 \pi \mathrm{N}\)
3 \(0.4 \pi \mathrm{N}\)
4 \(0.8 \pi \mathrm{N}\)
Rotational Motion

150118 A thin wire of length ' \(L\) ' and uniform linear mass density ' \(m\) ' is bent into a circular loop. The moment of inertia of this loop about the tangential axis and in the plane of the coil is

1 \(\frac{3 \mathrm{~mL}^{3}}{4 \pi^{2}}\)
2 \(\frac{3 \mathrm{~mL}^{3}}{8 \pi^{2}}\)
3 \(\frac{3 \mathrm{~mL}^{3}}{16 \pi^{2}}\)
4 \(\frac{3 \mathrm{~mL}^{3}}{2 \pi^{2}}\)
[МHT-CET 2020]
Rotational Motion

150119 A solid sphere has mass ' \(M\) ' and radius ' \(R\) '. Its moment of inertia about a parallel axis passing through a point at a distance \(\frac{R}{2}\) from its centre
is

1 \(\frac{13}{20} \mathrm{MR}^{2}\)
2 \(\frac{8}{11} \mathrm{MR}^{2}\)
3 \(\frac{11}{15} \mathrm{MR}^{2}\)
4 \(\frac{6}{10} \mathrm{MR}^{2}\)
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here