ROTATIONAL INERTIAOF SOLID BODIES
Rotational Motion

269568 From a uniform wire two circular loops are made (i) \(P\) of radius \(r\) and (ii) \(Q\) of radius \(n\). If the moment of inertia of \(Q\) about an axis passing through its centre and perpendicular to its plane is \(\mathbf{8}\) times that of \(\mathbf{P}\) about a similar axis. The value of \(n\) is (diameter of the wire is very much smaller than \(\mathrm{r}\) or \(\mathrm{nr}\) )

1 8
2 6
3 4
4 2
Rotational Motion

269569 The moment of inertia of a uniform thin rod of length \(L\) and mass \(M\) about an axis passing through a point at a distance of \(L / 3\) from one of its ends and perpendicular to the rod is

1 \(\frac{7 M L^{2}}{48}\)
2 \(\frac{M L^{2}}{6}\)
3 \(\frac{M L^{2}}{9}\)
4 \(\frac{M L^{2}}{3}\)
Rotational Motion

269570 Two small spheres of mass \(5 \mathrm{~kg}\) and \(15 \mathrm{~kg}\) are joined by a rod of length \(0.5 \mathrm{~m}\) and of negligible mass. The M.I. of the system about an axis passing through centre of rod and normal to it is

1 \(10 \mathrm{kgm}^{2}\)
2 \(1.25 \mathrm{kgm}^{2}\)
3 \(20 \mathrm{kgm}^{2}\)
4 \(8 \mathrm{kgm}^{2}\)
Rotational Motion

269571 Ratio of densities of materials of two circular discs of same mass and thickness is 5:6.The ratio of their M.I. about natural axes is

1 \(5: 6\)
2 \(6: 5\)
3 \(25: 36\)
4 \(1: 1\)
Rotational Motion

269568 From a uniform wire two circular loops are made (i) \(P\) of radius \(r\) and (ii) \(Q\) of radius \(n\). If the moment of inertia of \(Q\) about an axis passing through its centre and perpendicular to its plane is \(\mathbf{8}\) times that of \(\mathbf{P}\) about a similar axis. The value of \(n\) is (diameter of the wire is very much smaller than \(\mathrm{r}\) or \(\mathrm{nr}\) )

1 8
2 6
3 4
4 2
Rotational Motion

269569 The moment of inertia of a uniform thin rod of length \(L\) and mass \(M\) about an axis passing through a point at a distance of \(L / 3\) from one of its ends and perpendicular to the rod is

1 \(\frac{7 M L^{2}}{48}\)
2 \(\frac{M L^{2}}{6}\)
3 \(\frac{M L^{2}}{9}\)
4 \(\frac{M L^{2}}{3}\)
Rotational Motion

269570 Two small spheres of mass \(5 \mathrm{~kg}\) and \(15 \mathrm{~kg}\) are joined by a rod of length \(0.5 \mathrm{~m}\) and of negligible mass. The M.I. of the system about an axis passing through centre of rod and normal to it is

1 \(10 \mathrm{kgm}^{2}\)
2 \(1.25 \mathrm{kgm}^{2}\)
3 \(20 \mathrm{kgm}^{2}\)
4 \(8 \mathrm{kgm}^{2}\)
Rotational Motion

269571 Ratio of densities of materials of two circular discs of same mass and thickness is 5:6.The ratio of their M.I. about natural axes is

1 \(5: 6\)
2 \(6: 5\)
3 \(25: 36\)
4 \(1: 1\)
Rotational Motion

269568 From a uniform wire two circular loops are made (i) \(P\) of radius \(r\) and (ii) \(Q\) of radius \(n\). If the moment of inertia of \(Q\) about an axis passing through its centre and perpendicular to its plane is \(\mathbf{8}\) times that of \(\mathbf{P}\) about a similar axis. The value of \(n\) is (diameter of the wire is very much smaller than \(\mathrm{r}\) or \(\mathrm{nr}\) )

1 8
2 6
3 4
4 2
Rotational Motion

269569 The moment of inertia of a uniform thin rod of length \(L\) and mass \(M\) about an axis passing through a point at a distance of \(L / 3\) from one of its ends and perpendicular to the rod is

1 \(\frac{7 M L^{2}}{48}\)
2 \(\frac{M L^{2}}{6}\)
3 \(\frac{M L^{2}}{9}\)
4 \(\frac{M L^{2}}{3}\)
Rotational Motion

269570 Two small spheres of mass \(5 \mathrm{~kg}\) and \(15 \mathrm{~kg}\) are joined by a rod of length \(0.5 \mathrm{~m}\) and of negligible mass. The M.I. of the system about an axis passing through centre of rod and normal to it is

1 \(10 \mathrm{kgm}^{2}\)
2 \(1.25 \mathrm{kgm}^{2}\)
3 \(20 \mathrm{kgm}^{2}\)
4 \(8 \mathrm{kgm}^{2}\)
Rotational Motion

269571 Ratio of densities of materials of two circular discs of same mass and thickness is 5:6.The ratio of their M.I. about natural axes is

1 \(5: 6\)
2 \(6: 5\)
3 \(25: 36\)
4 \(1: 1\)
Rotational Motion

269568 From a uniform wire two circular loops are made (i) \(P\) of radius \(r\) and (ii) \(Q\) of radius \(n\). If the moment of inertia of \(Q\) about an axis passing through its centre and perpendicular to its plane is \(\mathbf{8}\) times that of \(\mathbf{P}\) about a similar axis. The value of \(n\) is (diameter of the wire is very much smaller than \(\mathrm{r}\) or \(\mathrm{nr}\) )

1 8
2 6
3 4
4 2
Rotational Motion

269569 The moment of inertia of a uniform thin rod of length \(L\) and mass \(M\) about an axis passing through a point at a distance of \(L / 3\) from one of its ends and perpendicular to the rod is

1 \(\frac{7 M L^{2}}{48}\)
2 \(\frac{M L^{2}}{6}\)
3 \(\frac{M L^{2}}{9}\)
4 \(\frac{M L^{2}}{3}\)
Rotational Motion

269570 Two small spheres of mass \(5 \mathrm{~kg}\) and \(15 \mathrm{~kg}\) are joined by a rod of length \(0.5 \mathrm{~m}\) and of negligible mass. The M.I. of the system about an axis passing through centre of rod and normal to it is

1 \(10 \mathrm{kgm}^{2}\)
2 \(1.25 \mathrm{kgm}^{2}\)
3 \(20 \mathrm{kgm}^{2}\)
4 \(8 \mathrm{kgm}^{2}\)
Rotational Motion

269571 Ratio of densities of materials of two circular discs of same mass and thickness is 5:6.The ratio of their M.I. about natural axes is

1 \(5: 6\)
2 \(6: 5\)
3 \(25: 36\)
4 \(1: 1\)