00. Centre of Mass
Rotational Motion

149688 Two atoms of oxygen are located at \(\mathbf{r}_{1}\) and \(\mathbf{r}_{2}\) Their centre of mass is at

1 \(r_{1}+r_{2}\)
2 \(\frac{r_{1}-r_{2}}{2}\)
3 \(\frac{r_{1}+r_{2}}{2}\)
4 \(r_{1}-r_{2}\)
Rotational Motion

149689 Four identical spheres each of radius \(10 \mathrm{~m}\) and equal mass \(1 \mathrm{~kg}\) each are placed on a horizontal surface touching each other, so that their centre are located at the vertices of a square of side \(20 \mathrm{~cm}\). What is the distance of their centre of mass from the centre of either sphere?

1 \(20 \sqrt{2}\)
2 \(30 \sqrt{2}\)
3 \(10 \sqrt{2}\)
4 \(40 \sqrt{2}\)
Rotational Motion

149690 A uniform circular disc has radius \(r\). A square portion of diagonal \(r\) is cut from it. The centre of mass of the remaining disc from the centre of disc is

1 \(\frac{r}{2-4 \pi}\)
2 \(\frac{r}{3-3 \pi}\)
3 \(\frac{r}{2-5 \pi}\)
4 \(\frac{2 r}{1-2 \pi}\)
Rotational Motion

149691 A thin disc and a thin ring, both have mass \(M\) and radius \(R\). Both rotate about axis through their center of mass and are perpendicular to their surfaces at the same angular velocity. Which of the following is true?

1 The ring has higher kinetic energy
2 The disc has higher kinetic energy
3 The ring and the disc have the same kinetic energy
4 Kinetic energies of both the bodies are zero since they are not in linear motion
Rotational Motion

149688 Two atoms of oxygen are located at \(\mathbf{r}_{1}\) and \(\mathbf{r}_{2}\) Their centre of mass is at

1 \(r_{1}+r_{2}\)
2 \(\frac{r_{1}-r_{2}}{2}\)
3 \(\frac{r_{1}+r_{2}}{2}\)
4 \(r_{1}-r_{2}\)
Rotational Motion

149689 Four identical spheres each of radius \(10 \mathrm{~m}\) and equal mass \(1 \mathrm{~kg}\) each are placed on a horizontal surface touching each other, so that their centre are located at the vertices of a square of side \(20 \mathrm{~cm}\). What is the distance of their centre of mass from the centre of either sphere?

1 \(20 \sqrt{2}\)
2 \(30 \sqrt{2}\)
3 \(10 \sqrt{2}\)
4 \(40 \sqrt{2}\)
Rotational Motion

149690 A uniform circular disc has radius \(r\). A square portion of diagonal \(r\) is cut from it. The centre of mass of the remaining disc from the centre of disc is

1 \(\frac{r}{2-4 \pi}\)
2 \(\frac{r}{3-3 \pi}\)
3 \(\frac{r}{2-5 \pi}\)
4 \(\frac{2 r}{1-2 \pi}\)
Rotational Motion

149691 A thin disc and a thin ring, both have mass \(M\) and radius \(R\). Both rotate about axis through their center of mass and are perpendicular to their surfaces at the same angular velocity. Which of the following is true?

1 The ring has higher kinetic energy
2 The disc has higher kinetic energy
3 The ring and the disc have the same kinetic energy
4 Kinetic energies of both the bodies are zero since they are not in linear motion
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Rotational Motion

149688 Two atoms of oxygen are located at \(\mathbf{r}_{1}\) and \(\mathbf{r}_{2}\) Their centre of mass is at

1 \(r_{1}+r_{2}\)
2 \(\frac{r_{1}-r_{2}}{2}\)
3 \(\frac{r_{1}+r_{2}}{2}\)
4 \(r_{1}-r_{2}\)
Rotational Motion

149689 Four identical spheres each of radius \(10 \mathrm{~m}\) and equal mass \(1 \mathrm{~kg}\) each are placed on a horizontal surface touching each other, so that their centre are located at the vertices of a square of side \(20 \mathrm{~cm}\). What is the distance of their centre of mass from the centre of either sphere?

1 \(20 \sqrt{2}\)
2 \(30 \sqrt{2}\)
3 \(10 \sqrt{2}\)
4 \(40 \sqrt{2}\)
Rotational Motion

149690 A uniform circular disc has radius \(r\). A square portion of diagonal \(r\) is cut from it. The centre of mass of the remaining disc from the centre of disc is

1 \(\frac{r}{2-4 \pi}\)
2 \(\frac{r}{3-3 \pi}\)
3 \(\frac{r}{2-5 \pi}\)
4 \(\frac{2 r}{1-2 \pi}\)
Rotational Motion

149691 A thin disc and a thin ring, both have mass \(M\) and radius \(R\). Both rotate about axis through their center of mass and are perpendicular to their surfaces at the same angular velocity. Which of the following is true?

1 The ring has higher kinetic energy
2 The disc has higher kinetic energy
3 The ring and the disc have the same kinetic energy
4 Kinetic energies of both the bodies are zero since they are not in linear motion
Rotational Motion

149688 Two atoms of oxygen are located at \(\mathbf{r}_{1}\) and \(\mathbf{r}_{2}\) Their centre of mass is at

1 \(r_{1}+r_{2}\)
2 \(\frac{r_{1}-r_{2}}{2}\)
3 \(\frac{r_{1}+r_{2}}{2}\)
4 \(r_{1}-r_{2}\)
Rotational Motion

149689 Four identical spheres each of radius \(10 \mathrm{~m}\) and equal mass \(1 \mathrm{~kg}\) each are placed on a horizontal surface touching each other, so that their centre are located at the vertices of a square of side \(20 \mathrm{~cm}\). What is the distance of their centre of mass from the centre of either sphere?

1 \(20 \sqrt{2}\)
2 \(30 \sqrt{2}\)
3 \(10 \sqrt{2}\)
4 \(40 \sqrt{2}\)
Rotational Motion

149690 A uniform circular disc has radius \(r\). A square portion of diagonal \(r\) is cut from it. The centre of mass of the remaining disc from the centre of disc is

1 \(\frac{r}{2-4 \pi}\)
2 \(\frac{r}{3-3 \pi}\)
3 \(\frac{r}{2-5 \pi}\)
4 \(\frac{2 r}{1-2 \pi}\)
Rotational Motion

149691 A thin disc and a thin ring, both have mass \(M\) and radius \(R\). Both rotate about axis through their center of mass and are perpendicular to their surfaces at the same angular velocity. Which of the following is true?

1 The ring has higher kinetic energy
2 The disc has higher kinetic energy
3 The ring and the disc have the same kinetic energy
4 Kinetic energies of both the bodies are zero since they are not in linear motion