00. Centre of Mass
Rotational Motion

149766 Three particles each of mass \(1 \mathrm{~kg}\) are placed at the corners of a right angled triangle \(A O B . O\) Being the origin of the coordinate system \((\mathrm{OA}\) and \(O B\) ) along positive \(X\)-direction and positive Y-direction). If \(\mathrm{OA}=\mathrm{OB}=1 \mathrm{~m}\), the positive vector of the centre of mass (in meters) is:

1 \(\frac{\hat{i}+\hat{j}}{3}\)
2 \(\frac{\hat{i}-\hat{j}}{3}\)
3 \(\frac{2(\hat{\mathrm{i}}+\hat{\mathrm{j}})}{3}\)
4 \((\hat{\mathrm{i}}-\hat{\mathrm{j}})\)
Rotational Motion

149767 Four particles, each of mass \(1 \mathrm{~kg}\), are placed at the corners of a square of side \(1 \mathrm{~m}\) in the \(X-Y\) plane. If the point of intersection of the diagonals of the square, is taken as the origin, the co-ordinates of the centre of mass are:

1 \((1,1)\)
2 \((-1,1)\)
3 \((1,-1)\)
4 \((0,0)\)
Rotational Motion

149768 One end of a thin uniform rod of length \(L\) and mass \(M_{1}\) is riveted to the centre of a uniform circular disc of radius \(r\) and mass \(M_{2}\), so that both are coplanar. The centre of mass of the combination from the centre of the disc is:

1 \(\frac{L\left(M_{1}+M_{2}\right)}{2 M_{1}}\)
2 \(\frac{\mathrm{LM}_{1}}{2\left(\mathrm{M}_{1}+\mathrm{M}_{2}\right)}\)
3 \(\frac{2\left(\mathrm{M}_{1}+\mathrm{M}_{2}\right)}{\mathrm{LM}_{1}}\)
4 \(\frac{2 \mathrm{LM}_{1}}{\left(\mathrm{M}_{1}+\mathrm{M}_{2}\right)}\)
Rotational Motion

149769 A uniform rod of length one meter is bent at its midpoint to make \(90^{\circ}\) angle. The distance of the centre of mass from the centre of rod is:

1 \(36.1 \mathrm{~cm}\)
2 \(25.2 \mathrm{~cm}\)
3 \(17.7 \mathrm{~cm}\)
4 zero
Rotational Motion

149766 Three particles each of mass \(1 \mathrm{~kg}\) are placed at the corners of a right angled triangle \(A O B . O\) Being the origin of the coordinate system \((\mathrm{OA}\) and \(O B\) ) along positive \(X\)-direction and positive Y-direction). If \(\mathrm{OA}=\mathrm{OB}=1 \mathrm{~m}\), the positive vector of the centre of mass (in meters) is:

1 \(\frac{\hat{i}+\hat{j}}{3}\)
2 \(\frac{\hat{i}-\hat{j}}{3}\)
3 \(\frac{2(\hat{\mathrm{i}}+\hat{\mathrm{j}})}{3}\)
4 \((\hat{\mathrm{i}}-\hat{\mathrm{j}})\)
Rotational Motion

149767 Four particles, each of mass \(1 \mathrm{~kg}\), are placed at the corners of a square of side \(1 \mathrm{~m}\) in the \(X-Y\) plane. If the point of intersection of the diagonals of the square, is taken as the origin, the co-ordinates of the centre of mass are:

1 \((1,1)\)
2 \((-1,1)\)
3 \((1,-1)\)
4 \((0,0)\)
Rotational Motion

149768 One end of a thin uniform rod of length \(L\) and mass \(M_{1}\) is riveted to the centre of a uniform circular disc of radius \(r\) and mass \(M_{2}\), so that both are coplanar. The centre of mass of the combination from the centre of the disc is:

1 \(\frac{L\left(M_{1}+M_{2}\right)}{2 M_{1}}\)
2 \(\frac{\mathrm{LM}_{1}}{2\left(\mathrm{M}_{1}+\mathrm{M}_{2}\right)}\)
3 \(\frac{2\left(\mathrm{M}_{1}+\mathrm{M}_{2}\right)}{\mathrm{LM}_{1}}\)
4 \(\frac{2 \mathrm{LM}_{1}}{\left(\mathrm{M}_{1}+\mathrm{M}_{2}\right)}\)
Rotational Motion

149769 A uniform rod of length one meter is bent at its midpoint to make \(90^{\circ}\) angle. The distance of the centre of mass from the centre of rod is:

1 \(36.1 \mathrm{~cm}\)
2 \(25.2 \mathrm{~cm}\)
3 \(17.7 \mathrm{~cm}\)
4 zero
Rotational Motion

149766 Three particles each of mass \(1 \mathrm{~kg}\) are placed at the corners of a right angled triangle \(A O B . O\) Being the origin of the coordinate system \((\mathrm{OA}\) and \(O B\) ) along positive \(X\)-direction and positive Y-direction). If \(\mathrm{OA}=\mathrm{OB}=1 \mathrm{~m}\), the positive vector of the centre of mass (in meters) is:

1 \(\frac{\hat{i}+\hat{j}}{3}\)
2 \(\frac{\hat{i}-\hat{j}}{3}\)
3 \(\frac{2(\hat{\mathrm{i}}+\hat{\mathrm{j}})}{3}\)
4 \((\hat{\mathrm{i}}-\hat{\mathrm{j}})\)
Rotational Motion

149767 Four particles, each of mass \(1 \mathrm{~kg}\), are placed at the corners of a square of side \(1 \mathrm{~m}\) in the \(X-Y\) plane. If the point of intersection of the diagonals of the square, is taken as the origin, the co-ordinates of the centre of mass are:

1 \((1,1)\)
2 \((-1,1)\)
3 \((1,-1)\)
4 \((0,0)\)
Rotational Motion

149768 One end of a thin uniform rod of length \(L\) and mass \(M_{1}\) is riveted to the centre of a uniform circular disc of radius \(r\) and mass \(M_{2}\), so that both are coplanar. The centre of mass of the combination from the centre of the disc is:

1 \(\frac{L\left(M_{1}+M_{2}\right)}{2 M_{1}}\)
2 \(\frac{\mathrm{LM}_{1}}{2\left(\mathrm{M}_{1}+\mathrm{M}_{2}\right)}\)
3 \(\frac{2\left(\mathrm{M}_{1}+\mathrm{M}_{2}\right)}{\mathrm{LM}_{1}}\)
4 \(\frac{2 \mathrm{LM}_{1}}{\left(\mathrm{M}_{1}+\mathrm{M}_{2}\right)}\)
Rotational Motion

149769 A uniform rod of length one meter is bent at its midpoint to make \(90^{\circ}\) angle. The distance of the centre of mass from the centre of rod is:

1 \(36.1 \mathrm{~cm}\)
2 \(25.2 \mathrm{~cm}\)
3 \(17.7 \mathrm{~cm}\)
4 zero
Rotational Motion

149766 Three particles each of mass \(1 \mathrm{~kg}\) are placed at the corners of a right angled triangle \(A O B . O\) Being the origin of the coordinate system \((\mathrm{OA}\) and \(O B\) ) along positive \(X\)-direction and positive Y-direction). If \(\mathrm{OA}=\mathrm{OB}=1 \mathrm{~m}\), the positive vector of the centre of mass (in meters) is:

1 \(\frac{\hat{i}+\hat{j}}{3}\)
2 \(\frac{\hat{i}-\hat{j}}{3}\)
3 \(\frac{2(\hat{\mathrm{i}}+\hat{\mathrm{j}})}{3}\)
4 \((\hat{\mathrm{i}}-\hat{\mathrm{j}})\)
Rotational Motion

149767 Four particles, each of mass \(1 \mathrm{~kg}\), are placed at the corners of a square of side \(1 \mathrm{~m}\) in the \(X-Y\) plane. If the point of intersection of the diagonals of the square, is taken as the origin, the co-ordinates of the centre of mass are:

1 \((1,1)\)
2 \((-1,1)\)
3 \((1,-1)\)
4 \((0,0)\)
Rotational Motion

149768 One end of a thin uniform rod of length \(L\) and mass \(M_{1}\) is riveted to the centre of a uniform circular disc of radius \(r\) and mass \(M_{2}\), so that both are coplanar. The centre of mass of the combination from the centre of the disc is:

1 \(\frac{L\left(M_{1}+M_{2}\right)}{2 M_{1}}\)
2 \(\frac{\mathrm{LM}_{1}}{2\left(\mathrm{M}_{1}+\mathrm{M}_{2}\right)}\)
3 \(\frac{2\left(\mathrm{M}_{1}+\mathrm{M}_{2}\right)}{\mathrm{LM}_{1}}\)
4 \(\frac{2 \mathrm{LM}_{1}}{\left(\mathrm{M}_{1}+\mathrm{M}_{2}\right)}\)
Rotational Motion

149769 A uniform rod of length one meter is bent at its midpoint to make \(90^{\circ}\) angle. The distance of the centre of mass from the centre of rod is:

1 \(36.1 \mathrm{~cm}\)
2 \(25.2 \mathrm{~cm}\)
3 \(17.7 \mathrm{~cm}\)
4 zero