03. Moment of Inertia, Radius of Gyration
Rotational Motion

150175 A circular coil of radius \(9 \mathrm{~cm}\) carrying a current of \(2 \mathrm{~A}\) is free to rotate about an axis in its plane perpendicular to an external magnetic field of \(\pi \times 10^{-2} \mathrm{~T}\). When the coil is tuned slightly and released, it oscillates about its stable equilibrium with a time period of \(\frac{1}{3} \mathrm{~s}\). If the moment of inertia of the coil about its axis of rotation is \(9 \times 10^{-5} \mathbf{k g m}^{2}\), the number of turns of the coil is

1 10
2 20
3 30
4 40
Rotational Motion

150176 A small hole is made in a circular disc of mass ' \(M\) ' and radius ' \(R\) ' at a distance of \(\frac{R}{4}\) from the centre. The disc is supported on a horizontal peg through this hole. The moment of inertia of the disc about the horizontal peg is

1 \(\frac{9 \mathrm{MR}^{2}}{16}\)
2 \(\frac{5 \mathrm{MR}^{2}}{4}\)
3 \(\frac{5 \mathrm{MR}^{2}}{16}\)
4 \(\frac{\mathrm{MR}^{2}}{9}\)
Rotational Motion

150177 A solid cylinder of mass \(M\) and radius \(R\) rolls on a flat surface. Find its moment of inertia about the line of contact

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

150178 A body of mass \(5 \mathrm{~kg}\) acquires an angular acceleration of \(10 \mathrm{rad} \mathrm{s}^{-2}\) by an applied torque of \(2 \mathbf{N ~ m}\). Find its radius of gyration.

1 \(2.5 \mathrm{~m}\)
2 \(\sqrt{2.5} \mathrm{~m}\)
3 \(\sqrt{0.2} \mathrm{~m}\)
4 \(0.2 \mathrm{~m}\)
Rotational Motion

150175 A circular coil of radius \(9 \mathrm{~cm}\) carrying a current of \(2 \mathrm{~A}\) is free to rotate about an axis in its plane perpendicular to an external magnetic field of \(\pi \times 10^{-2} \mathrm{~T}\). When the coil is tuned slightly and released, it oscillates about its stable equilibrium with a time period of \(\frac{1}{3} \mathrm{~s}\). If the moment of inertia of the coil about its axis of rotation is \(9 \times 10^{-5} \mathbf{k g m}^{2}\), the number of turns of the coil is

1 10
2 20
3 30
4 40
Rotational Motion

150176 A small hole is made in a circular disc of mass ' \(M\) ' and radius ' \(R\) ' at a distance of \(\frac{R}{4}\) from the centre. The disc is supported on a horizontal peg through this hole. The moment of inertia of the disc about the horizontal peg is

1 \(\frac{9 \mathrm{MR}^{2}}{16}\)
2 \(\frac{5 \mathrm{MR}^{2}}{4}\)
3 \(\frac{5 \mathrm{MR}^{2}}{16}\)
4 \(\frac{\mathrm{MR}^{2}}{9}\)
Rotational Motion

150177 A solid cylinder of mass \(M\) and radius \(R\) rolls on a flat surface. Find its moment of inertia about the line of contact

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

150178 A body of mass \(5 \mathrm{~kg}\) acquires an angular acceleration of \(10 \mathrm{rad} \mathrm{s}^{-2}\) by an applied torque of \(2 \mathbf{N ~ m}\). Find its radius of gyration.

1 \(2.5 \mathrm{~m}\)
2 \(\sqrt{2.5} \mathrm{~m}\)
3 \(\sqrt{0.2} \mathrm{~m}\)
4 \(0.2 \mathrm{~m}\)
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Rotational Motion

150175 A circular coil of radius \(9 \mathrm{~cm}\) carrying a current of \(2 \mathrm{~A}\) is free to rotate about an axis in its plane perpendicular to an external magnetic field of \(\pi \times 10^{-2} \mathrm{~T}\). When the coil is tuned slightly and released, it oscillates about its stable equilibrium with a time period of \(\frac{1}{3} \mathrm{~s}\). If the moment of inertia of the coil about its axis of rotation is \(9 \times 10^{-5} \mathbf{k g m}^{2}\), the number of turns of the coil is

1 10
2 20
3 30
4 40
Rotational Motion

150176 A small hole is made in a circular disc of mass ' \(M\) ' and radius ' \(R\) ' at a distance of \(\frac{R}{4}\) from the centre. The disc is supported on a horizontal peg through this hole. The moment of inertia of the disc about the horizontal peg is

1 \(\frac{9 \mathrm{MR}^{2}}{16}\)
2 \(\frac{5 \mathrm{MR}^{2}}{4}\)
3 \(\frac{5 \mathrm{MR}^{2}}{16}\)
4 \(\frac{\mathrm{MR}^{2}}{9}\)
Rotational Motion

150177 A solid cylinder of mass \(M\) and radius \(R\) rolls on a flat surface. Find its moment of inertia about the line of contact

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

150178 A body of mass \(5 \mathrm{~kg}\) acquires an angular acceleration of \(10 \mathrm{rad} \mathrm{s}^{-2}\) by an applied torque of \(2 \mathbf{N ~ m}\). Find its radius of gyration.

1 \(2.5 \mathrm{~m}\)
2 \(\sqrt{2.5} \mathrm{~m}\)
3 \(\sqrt{0.2} \mathrm{~m}\)
4 \(0.2 \mathrm{~m}\)
Rotational Motion

150175 A circular coil of radius \(9 \mathrm{~cm}\) carrying a current of \(2 \mathrm{~A}\) is free to rotate about an axis in its plane perpendicular to an external magnetic field of \(\pi \times 10^{-2} \mathrm{~T}\). When the coil is tuned slightly and released, it oscillates about its stable equilibrium with a time period of \(\frac{1}{3} \mathrm{~s}\). If the moment of inertia of the coil about its axis of rotation is \(9 \times 10^{-5} \mathbf{k g m}^{2}\), the number of turns of the coil is

1 10
2 20
3 30
4 40
Rotational Motion

150176 A small hole is made in a circular disc of mass ' \(M\) ' and radius ' \(R\) ' at a distance of \(\frac{R}{4}\) from the centre. The disc is supported on a horizontal peg through this hole. The moment of inertia of the disc about the horizontal peg is

1 \(\frac{9 \mathrm{MR}^{2}}{16}\)
2 \(\frac{5 \mathrm{MR}^{2}}{4}\)
3 \(\frac{5 \mathrm{MR}^{2}}{16}\)
4 \(\frac{\mathrm{MR}^{2}}{9}\)
Rotational Motion

150177 A solid cylinder of mass \(M\) and radius \(R\) rolls on a flat surface. Find its moment of inertia about the line of contact

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

150178 A body of mass \(5 \mathrm{~kg}\) acquires an angular acceleration of \(10 \mathrm{rad} \mathrm{s}^{-2}\) by an applied torque of \(2 \mathbf{N ~ m}\). Find its radius of gyration.

1 \(2.5 \mathrm{~m}\)
2 \(\sqrt{2.5} \mathrm{~m}\)
3 \(\sqrt{0.2} \mathrm{~m}\)
4 \(0.2 \mathrm{~m}\)