03. Moment of Inertia, Radius of Gyration
Rotational Motion

150147 A rod of length \(L\) is composed of a uniform length \(\frac{L}{2}\) of wood whose mass is \(m_{w}\) and an uniform length \(\frac{L}{2}\) of brass whose mass is \(m_{b}\).
The moment of inertia I of the rod about an axis perpendicular to the rod and through its centre is equal to

1 \(\left(m_{w}+m_{b}\right) \frac{L^{2}}{6}\)
2 \(\left(m_{w}+m_{b}\right) \frac{L^{2}}{2}\)
3 \(\left(\mathrm{m}_{\mathrm{w}}+\mathrm{m}_{\mathrm{b}}\right) \frac{\mathrm{L}^{2}}{12}\)
4 \(\left(\mathrm{m}_{\mathrm{w}}+\mathrm{m}_{\mathrm{b}}\right) \frac{\mathrm{L}^{2}}{3}\)
Rotational Motion

150148 M.I of a circular loop of radius \(R\) about the axis in figure is
original image

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

150149 If the radius of a sphere is doubled by keeping its mass constant, compare the moment of inertia of the old sphere with that of the new sphere, about any diameter.

1 \(I_{1}: I_{2}=1: 4\)
2 \(I_{1}: I_{2}=1: 2\)
3 \(\mathrm{I}_{1}: \mathrm{I}_{2}=4: 1\)
4 \(I_{1}: I_{2}=2: 1\)
Rotational Motion

150150 A body of mass \(5 \mathrm{~kg}\) acquires an acceleration of \(10 \mathrm{rads}^{-2}\) due to an applied torque of \(2 \mathrm{Nm}\). Its radius of gyration is

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

150147 A rod of length \(L\) is composed of a uniform length \(\frac{L}{2}\) of wood whose mass is \(m_{w}\) and an uniform length \(\frac{L}{2}\) of brass whose mass is \(m_{b}\).
The moment of inertia I of the rod about an axis perpendicular to the rod and through its centre is equal to

1 \(\left(m_{w}+m_{b}\right) \frac{L^{2}}{6}\)
2 \(\left(m_{w}+m_{b}\right) \frac{L^{2}}{2}\)
3 \(\left(\mathrm{m}_{\mathrm{w}}+\mathrm{m}_{\mathrm{b}}\right) \frac{\mathrm{L}^{2}}{12}\)
4 \(\left(\mathrm{m}_{\mathrm{w}}+\mathrm{m}_{\mathrm{b}}\right) \frac{\mathrm{L}^{2}}{3}\)
Rotational Motion

150148 M.I of a circular loop of radius \(R\) about the axis in figure is
original image

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

150149 If the radius of a sphere is doubled by keeping its mass constant, compare the moment of inertia of the old sphere with that of the new sphere, about any diameter.

1 \(I_{1}: I_{2}=1: 4\)
2 \(I_{1}: I_{2}=1: 2\)
3 \(\mathrm{I}_{1}: \mathrm{I}_{2}=4: 1\)
4 \(I_{1}: I_{2}=2: 1\)
Rotational Motion

150150 A body of mass \(5 \mathrm{~kg}\) acquires an acceleration of \(10 \mathrm{rads}^{-2}\) due to an applied torque of \(2 \mathrm{Nm}\). Its radius of gyration is

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

150147 A rod of length \(L\) is composed of a uniform length \(\frac{L}{2}\) of wood whose mass is \(m_{w}\) and an uniform length \(\frac{L}{2}\) of brass whose mass is \(m_{b}\).
The moment of inertia I of the rod about an axis perpendicular to the rod and through its centre is equal to

1 \(\left(m_{w}+m_{b}\right) \frac{L^{2}}{6}\)
2 \(\left(m_{w}+m_{b}\right) \frac{L^{2}}{2}\)
3 \(\left(\mathrm{m}_{\mathrm{w}}+\mathrm{m}_{\mathrm{b}}\right) \frac{\mathrm{L}^{2}}{12}\)
4 \(\left(\mathrm{m}_{\mathrm{w}}+\mathrm{m}_{\mathrm{b}}\right) \frac{\mathrm{L}^{2}}{3}\)
Rotational Motion

150148 M.I of a circular loop of radius \(R\) about the axis in figure is
original image

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

150149 If the radius of a sphere is doubled by keeping its mass constant, compare the moment of inertia of the old sphere with that of the new sphere, about any diameter.

1 \(I_{1}: I_{2}=1: 4\)
2 \(I_{1}: I_{2}=1: 2\)
3 \(\mathrm{I}_{1}: \mathrm{I}_{2}=4: 1\)
4 \(I_{1}: I_{2}=2: 1\)
Rotational Motion

150150 A body of mass \(5 \mathrm{~kg}\) acquires an acceleration of \(10 \mathrm{rads}^{-2}\) due to an applied torque of \(2 \mathrm{Nm}\). Its radius of gyration is

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

150147 A rod of length \(L\) is composed of a uniform length \(\frac{L}{2}\) of wood whose mass is \(m_{w}\) and an uniform length \(\frac{L}{2}\) of brass whose mass is \(m_{b}\).
The moment of inertia I of the rod about an axis perpendicular to the rod and through its centre is equal to

1 \(\left(m_{w}+m_{b}\right) \frac{L^{2}}{6}\)
2 \(\left(m_{w}+m_{b}\right) \frac{L^{2}}{2}\)
3 \(\left(\mathrm{m}_{\mathrm{w}}+\mathrm{m}_{\mathrm{b}}\right) \frac{\mathrm{L}^{2}}{12}\)
4 \(\left(\mathrm{m}_{\mathrm{w}}+\mathrm{m}_{\mathrm{b}}\right) \frac{\mathrm{L}^{2}}{3}\)
Rotational Motion

150148 M.I of a circular loop of radius \(R\) about the axis in figure is
original image

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

150149 If the radius of a sphere is doubled by keeping its mass constant, compare the moment of inertia of the old sphere with that of the new sphere, about any diameter.

1 \(I_{1}: I_{2}=1: 4\)
2 \(I_{1}: I_{2}=1: 2\)
3 \(\mathrm{I}_{1}: \mathrm{I}_{2}=4: 1\)
4 \(I_{1}: I_{2}=2: 1\)
Rotational Motion

150150 A body of mass \(5 \mathrm{~kg}\) acquires an acceleration of \(10 \mathrm{rads}^{-2}\) due to an applied torque of \(2 \mathrm{Nm}\). Its radius of gyration is

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