05. Rotational Motion and Rotational Energy
Rotational Motion

150310 A solid metal ring and a disc of same radius and mass are rotating about their diameters with same angular frequency. The ratio of their respective rotational kinetic energy values is

1 \(1: 1\)
2 \(1: 2\)
3 \(2: 1\)
4 \(1: 4\)
5 \(4: 1\)
Rotational Motion

150313 As solid of mass ' \(M\) ' and radius ' \(R\) ' spins about an axis passing through its centre making 600 rpm. Its kinetic energy of rotation is

1 \(\frac{2 \pi^{2}}{5} \mathrm{MR}\)
2 \(\frac{2 \pi}{5} M^{2} R^{2}\)
3 \(80 \pi \mathrm{MR}\)
4 \(80 \pi^{2} \mathrm{MR}^{2}\)
Rotational Motion

150314 A wheel of mass \(10 \mathrm{~kg}\), radius of gyration 50 \(\mathrm{cm}\) is rotating at \(300 \mathrm{rpm}\). The rotational kinetic energy of the wheel is

1 \(625 \mathrm{~J}\)
2 \(1000 \mathrm{~J}\)
3 \(1250 \mathrm{~J}\)
4 \(1500 \mathrm{~J}\)
Rotational Motion

150315 A thin uniform rod of mass \(1 \mathrm{~kg}\) and length \(1 \mathrm{~m}\) is hanged at one end to the ground floor. It originally stands vertically and allowed to fall ground. If the rod hits the ground with angular speed \(\omega\) then the correct statement is (Assume \(\mathbf{g}=\mathbf{1 0} \mathbf{~ m} / \mathrm{s}^{2}\)

1 \(\omega=\sqrt{30} \mathrm{rad} / \mathrm{s}\)
2 \(\omega=\sqrt{20} \mathrm{rad} / \mathrm{s}\)
3 \(\omega=5 \mathrm{rad} / \mathrm{s}\)
4 \(\omega=6 \mathrm{rad} / \mathrm{s}\)
Rotational Motion

150316 A molecule consists of two atoms each of mass ' \(m\) ' and separated by distance ' \(d\) '. At room temperature the average rotational kinetic energy is ' \(E\) ', then its angular frequency is

1 \(\frac{2}{\mathrm{~d}} \sqrt{\frac{\mathrm{E}}{\mathrm{m}}}\)
2 \(\sqrt{\frac{m}{E d}}\)
3 \(\frac{d}{2} \sqrt{\frac{m}{E}}\)
4 \(\sqrt{\frac{\mathrm{Ed}}{\mathrm{m}}}\)
Rotational Motion

150310 A solid metal ring and a disc of same radius and mass are rotating about their diameters with same angular frequency. The ratio of their respective rotational kinetic energy values is

1 \(1: 1\)
2 \(1: 2\)
3 \(2: 1\)
4 \(1: 4\)
5 \(4: 1\)
Rotational Motion

150313 As solid of mass ' \(M\) ' and radius ' \(R\) ' spins about an axis passing through its centre making 600 rpm. Its kinetic energy of rotation is

1 \(\frac{2 \pi^{2}}{5} \mathrm{MR}\)
2 \(\frac{2 \pi}{5} M^{2} R^{2}\)
3 \(80 \pi \mathrm{MR}\)
4 \(80 \pi^{2} \mathrm{MR}^{2}\)
Rotational Motion

150314 A wheel of mass \(10 \mathrm{~kg}\), radius of gyration 50 \(\mathrm{cm}\) is rotating at \(300 \mathrm{rpm}\). The rotational kinetic energy of the wheel is

1 \(625 \mathrm{~J}\)
2 \(1000 \mathrm{~J}\)
3 \(1250 \mathrm{~J}\)
4 \(1500 \mathrm{~J}\)
Rotational Motion

150315 A thin uniform rod of mass \(1 \mathrm{~kg}\) and length \(1 \mathrm{~m}\) is hanged at one end to the ground floor. It originally stands vertically and allowed to fall ground. If the rod hits the ground with angular speed \(\omega\) then the correct statement is (Assume \(\mathbf{g}=\mathbf{1 0} \mathbf{~ m} / \mathrm{s}^{2}\)

1 \(\omega=\sqrt{30} \mathrm{rad} / \mathrm{s}\)
2 \(\omega=\sqrt{20} \mathrm{rad} / \mathrm{s}\)
3 \(\omega=5 \mathrm{rad} / \mathrm{s}\)
4 \(\omega=6 \mathrm{rad} / \mathrm{s}\)
Rotational Motion

150316 A molecule consists of two atoms each of mass ' \(m\) ' and separated by distance ' \(d\) '. At room temperature the average rotational kinetic energy is ' \(E\) ', then its angular frequency is

1 \(\frac{2}{\mathrm{~d}} \sqrt{\frac{\mathrm{E}}{\mathrm{m}}}\)
2 \(\sqrt{\frac{m}{E d}}\)
3 \(\frac{d}{2} \sqrt{\frac{m}{E}}\)
4 \(\sqrt{\frac{\mathrm{Ed}}{\mathrm{m}}}\)
Rotational Motion

150310 A solid metal ring and a disc of same radius and mass are rotating about their diameters with same angular frequency. The ratio of their respective rotational kinetic energy values is

1 \(1: 1\)
2 \(1: 2\)
3 \(2: 1\)
4 \(1: 4\)
5 \(4: 1\)
Rotational Motion

150313 As solid of mass ' \(M\) ' and radius ' \(R\) ' spins about an axis passing through its centre making 600 rpm. Its kinetic energy of rotation is

1 \(\frac{2 \pi^{2}}{5} \mathrm{MR}\)
2 \(\frac{2 \pi}{5} M^{2} R^{2}\)
3 \(80 \pi \mathrm{MR}\)
4 \(80 \pi^{2} \mathrm{MR}^{2}\)
Rotational Motion

150314 A wheel of mass \(10 \mathrm{~kg}\), radius of gyration 50 \(\mathrm{cm}\) is rotating at \(300 \mathrm{rpm}\). The rotational kinetic energy of the wheel is

1 \(625 \mathrm{~J}\)
2 \(1000 \mathrm{~J}\)
3 \(1250 \mathrm{~J}\)
4 \(1500 \mathrm{~J}\)
Rotational Motion

150315 A thin uniform rod of mass \(1 \mathrm{~kg}\) and length \(1 \mathrm{~m}\) is hanged at one end to the ground floor. It originally stands vertically and allowed to fall ground. If the rod hits the ground with angular speed \(\omega\) then the correct statement is (Assume \(\mathbf{g}=\mathbf{1 0} \mathbf{~ m} / \mathrm{s}^{2}\)

1 \(\omega=\sqrt{30} \mathrm{rad} / \mathrm{s}\)
2 \(\omega=\sqrt{20} \mathrm{rad} / \mathrm{s}\)
3 \(\omega=5 \mathrm{rad} / \mathrm{s}\)
4 \(\omega=6 \mathrm{rad} / \mathrm{s}\)
Rotational Motion

150316 A molecule consists of two atoms each of mass ' \(m\) ' and separated by distance ' \(d\) '. At room temperature the average rotational kinetic energy is ' \(E\) ', then its angular frequency is

1 \(\frac{2}{\mathrm{~d}} \sqrt{\frac{\mathrm{E}}{\mathrm{m}}}\)
2 \(\sqrt{\frac{m}{E d}}\)
3 \(\frac{d}{2} \sqrt{\frac{m}{E}}\)
4 \(\sqrt{\frac{\mathrm{Ed}}{\mathrm{m}}}\)
Rotational Motion

150310 A solid metal ring and a disc of same radius and mass are rotating about their diameters with same angular frequency. The ratio of their respective rotational kinetic energy values is

1 \(1: 1\)
2 \(1: 2\)
3 \(2: 1\)
4 \(1: 4\)
5 \(4: 1\)
Rotational Motion

150313 As solid of mass ' \(M\) ' and radius ' \(R\) ' spins about an axis passing through its centre making 600 rpm. Its kinetic energy of rotation is

1 \(\frac{2 \pi^{2}}{5} \mathrm{MR}\)
2 \(\frac{2 \pi}{5} M^{2} R^{2}\)
3 \(80 \pi \mathrm{MR}\)
4 \(80 \pi^{2} \mathrm{MR}^{2}\)
Rotational Motion

150314 A wheel of mass \(10 \mathrm{~kg}\), radius of gyration 50 \(\mathrm{cm}\) is rotating at \(300 \mathrm{rpm}\). The rotational kinetic energy of the wheel is

1 \(625 \mathrm{~J}\)
2 \(1000 \mathrm{~J}\)
3 \(1250 \mathrm{~J}\)
4 \(1500 \mathrm{~J}\)
Rotational Motion

150315 A thin uniform rod of mass \(1 \mathrm{~kg}\) and length \(1 \mathrm{~m}\) is hanged at one end to the ground floor. It originally stands vertically and allowed to fall ground. If the rod hits the ground with angular speed \(\omega\) then the correct statement is (Assume \(\mathbf{g}=\mathbf{1 0} \mathbf{~ m} / \mathrm{s}^{2}\)

1 \(\omega=\sqrt{30} \mathrm{rad} / \mathrm{s}\)
2 \(\omega=\sqrt{20} \mathrm{rad} / \mathrm{s}\)
3 \(\omega=5 \mathrm{rad} / \mathrm{s}\)
4 \(\omega=6 \mathrm{rad} / \mathrm{s}\)
Rotational Motion

150316 A molecule consists of two atoms each of mass ' \(m\) ' and separated by distance ' \(d\) '. At room temperature the average rotational kinetic energy is ' \(E\) ', then its angular frequency is

1 \(\frac{2}{\mathrm{~d}} \sqrt{\frac{\mathrm{E}}{\mathrm{m}}}\)
2 \(\sqrt{\frac{m}{E d}}\)
3 \(\frac{d}{2} \sqrt{\frac{m}{E}}\)
4 \(\sqrt{\frac{\mathrm{Ed}}{\mathrm{m}}}\)
Rotational Motion

150310 A solid metal ring and a disc of same radius and mass are rotating about their diameters with same angular frequency. The ratio of their respective rotational kinetic energy values is

1 \(1: 1\)
2 \(1: 2\)
3 \(2: 1\)
4 \(1: 4\)
5 \(4: 1\)
Rotational Motion

150313 As solid of mass ' \(M\) ' and radius ' \(R\) ' spins about an axis passing through its centre making 600 rpm. Its kinetic energy of rotation is

1 \(\frac{2 \pi^{2}}{5} \mathrm{MR}\)
2 \(\frac{2 \pi}{5} M^{2} R^{2}\)
3 \(80 \pi \mathrm{MR}\)
4 \(80 \pi^{2} \mathrm{MR}^{2}\)
Rotational Motion

150314 A wheel of mass \(10 \mathrm{~kg}\), radius of gyration 50 \(\mathrm{cm}\) is rotating at \(300 \mathrm{rpm}\). The rotational kinetic energy of the wheel is

1 \(625 \mathrm{~J}\)
2 \(1000 \mathrm{~J}\)
3 \(1250 \mathrm{~J}\)
4 \(1500 \mathrm{~J}\)
Rotational Motion

150315 A thin uniform rod of mass \(1 \mathrm{~kg}\) and length \(1 \mathrm{~m}\) is hanged at one end to the ground floor. It originally stands vertically and allowed to fall ground. If the rod hits the ground with angular speed \(\omega\) then the correct statement is (Assume \(\mathbf{g}=\mathbf{1 0} \mathbf{~ m} / \mathrm{s}^{2}\)

1 \(\omega=\sqrt{30} \mathrm{rad} / \mathrm{s}\)
2 \(\omega=\sqrt{20} \mathrm{rad} / \mathrm{s}\)
3 \(\omega=5 \mathrm{rad} / \mathrm{s}\)
4 \(\omega=6 \mathrm{rad} / \mathrm{s}\)
Rotational Motion

150316 A molecule consists of two atoms each of mass ' \(m\) ' and separated by distance ' \(d\) '. At room temperature the average rotational kinetic energy is ' \(E\) ', then its angular frequency is

1 \(\frac{2}{\mathrm{~d}} \sqrt{\frac{\mathrm{E}}{\mathrm{m}}}\)
2 \(\sqrt{\frac{m}{E d}}\)
3 \(\frac{d}{2} \sqrt{\frac{m}{E}}\)
4 \(\sqrt{\frac{\mathrm{Ed}}{\mathrm{m}}}\)