00. Centre of Mass
Rotational Motion

149676 Two particles of mass \(5 \mathrm{~kg}\) and \(10 \quad \mathrm{~kg}\) respectively are attached to the two ends of a rigid rod of length \(1 \mathrm{~m}\) with negligible mass. The centre of mass of the system from the \(5 \mathbf{~ k g}\) particle is nearly at a distance of

1 \(50 \mathrm{~cm}\)
2 \(67 \mathrm{~cm}\)
3 \(80 \mathrm{~cm}\)
4 \(33 \mathrm{~cm}\)
Rotational Motion

149677 Three identical spheres, each of mass \(M\), are placed at the corners of a right angle triangle with the mutually perpendicular sides equal to \(2 \mathrm{~m}\) (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of centre of mass.

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

149681 Consider a two block system having masses \(M_{A}=3 \mathrm{~kg}\) and \(M_{B}=\mathbf{2 k g}\), as shown in the figure. If block \(A\) is pushed towards the centre of mass through a distance \(200 \mathrm{~cm}\), by what distance should the block \(B\) be moved so as to keep the centre of mass at the same position.

1 \(200 \mathrm{~cm}\)
2 \(300 \mathrm{~cm}\)
3 \(130 \mathrm{~cm}\)
4 \(250 \mathrm{~cm}\)
Rotational Motion

149682 A uniform wire of length ' \(L\) ' with centre of mass at the origin is lying along the \(x\)-axis. The wire is bent in the form of a circle such that its lowest point is at the origin. Then shift of centre of mass is

1 \(\frac{L}{\pi}\)
2 \(\frac{2 \mathrm{~L}}{\pi}\)
3 \(\frac{\mathrm{L}}{2 \pi}\)
4 \(\frac{\mathrm{L}}{3 \pi}\)
Rotational Motion

149680 Figure shows triangular lamina which can rotate about different axis of rotation. Moment of inertia is maximum about the axis

1 QR
2 PR
3 QS
4 PQ
Rotational Motion

149676 Two particles of mass \(5 \mathrm{~kg}\) and \(10 \quad \mathrm{~kg}\) respectively are attached to the two ends of a rigid rod of length \(1 \mathrm{~m}\) with negligible mass. The centre of mass of the system from the \(5 \mathbf{~ k g}\) particle is nearly at a distance of

1 \(50 \mathrm{~cm}\)
2 \(67 \mathrm{~cm}\)
3 \(80 \mathrm{~cm}\)
4 \(33 \mathrm{~cm}\)
Rotational Motion

149677 Three identical spheres, each of mass \(M\), are placed at the corners of a right angle triangle with the mutually perpendicular sides equal to \(2 \mathrm{~m}\) (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of centre of mass.

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

149681 Consider a two block system having masses \(M_{A}=3 \mathrm{~kg}\) and \(M_{B}=\mathbf{2 k g}\), as shown in the figure. If block \(A\) is pushed towards the centre of mass through a distance \(200 \mathrm{~cm}\), by what distance should the block \(B\) be moved so as to keep the centre of mass at the same position.

1 \(200 \mathrm{~cm}\)
2 \(300 \mathrm{~cm}\)
3 \(130 \mathrm{~cm}\)
4 \(250 \mathrm{~cm}\)
Rotational Motion

149682 A uniform wire of length ' \(L\) ' with centre of mass at the origin is lying along the \(x\)-axis. The wire is bent in the form of a circle such that its lowest point is at the origin. Then shift of centre of mass is

1 \(\frac{L}{\pi}\)
2 \(\frac{2 \mathrm{~L}}{\pi}\)
3 \(\frac{\mathrm{L}}{2 \pi}\)
4 \(\frac{\mathrm{L}}{3 \pi}\)
Rotational Motion

149680 Figure shows triangular lamina which can rotate about different axis of rotation. Moment of inertia is maximum about the axis

1 QR
2 PR
3 QS
4 PQ
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Rotational Motion

149676 Two particles of mass \(5 \mathrm{~kg}\) and \(10 \quad \mathrm{~kg}\) respectively are attached to the two ends of a rigid rod of length \(1 \mathrm{~m}\) with negligible mass. The centre of mass of the system from the \(5 \mathbf{~ k g}\) particle is nearly at a distance of

1 \(50 \mathrm{~cm}\)
2 \(67 \mathrm{~cm}\)
3 \(80 \mathrm{~cm}\)
4 \(33 \mathrm{~cm}\)
Rotational Motion

149677 Three identical spheres, each of mass \(M\), are placed at the corners of a right angle triangle with the mutually perpendicular sides equal to \(2 \mathrm{~m}\) (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of centre of mass.

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

149681 Consider a two block system having masses \(M_{A}=3 \mathrm{~kg}\) and \(M_{B}=\mathbf{2 k g}\), as shown in the figure. If block \(A\) is pushed towards the centre of mass through a distance \(200 \mathrm{~cm}\), by what distance should the block \(B\) be moved so as to keep the centre of mass at the same position.

1 \(200 \mathrm{~cm}\)
2 \(300 \mathrm{~cm}\)
3 \(130 \mathrm{~cm}\)
4 \(250 \mathrm{~cm}\)
Rotational Motion

149682 A uniform wire of length ' \(L\) ' with centre of mass at the origin is lying along the \(x\)-axis. The wire is bent in the form of a circle such that its lowest point is at the origin. Then shift of centre of mass is

1 \(\frac{L}{\pi}\)
2 \(\frac{2 \mathrm{~L}}{\pi}\)
3 \(\frac{\mathrm{L}}{2 \pi}\)
4 \(\frac{\mathrm{L}}{3 \pi}\)
Rotational Motion

149680 Figure shows triangular lamina which can rotate about different axis of rotation. Moment of inertia is maximum about the axis

1 QR
2 PR
3 QS
4 PQ
Rotational Motion

149676 Two particles of mass \(5 \mathrm{~kg}\) and \(10 \quad \mathrm{~kg}\) respectively are attached to the two ends of a rigid rod of length \(1 \mathrm{~m}\) with negligible mass. The centre of mass of the system from the \(5 \mathbf{~ k g}\) particle is nearly at a distance of

1 \(50 \mathrm{~cm}\)
2 \(67 \mathrm{~cm}\)
3 \(80 \mathrm{~cm}\)
4 \(33 \mathrm{~cm}\)
Rotational Motion

149677 Three identical spheres, each of mass \(M\), are placed at the corners of a right angle triangle with the mutually perpendicular sides equal to \(2 \mathrm{~m}\) (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of centre of mass.

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

149681 Consider a two block system having masses \(M_{A}=3 \mathrm{~kg}\) and \(M_{B}=\mathbf{2 k g}\), as shown in the figure. If block \(A\) is pushed towards the centre of mass through a distance \(200 \mathrm{~cm}\), by what distance should the block \(B\) be moved so as to keep the centre of mass at the same position.

1 \(200 \mathrm{~cm}\)
2 \(300 \mathrm{~cm}\)
3 \(130 \mathrm{~cm}\)
4 \(250 \mathrm{~cm}\)
Rotational Motion

149682 A uniform wire of length ' \(L\) ' with centre of mass at the origin is lying along the \(x\)-axis. The wire is bent in the form of a circle such that its lowest point is at the origin. Then shift of centre of mass is

1 \(\frac{L}{\pi}\)
2 \(\frac{2 \mathrm{~L}}{\pi}\)
3 \(\frac{\mathrm{L}}{2 \pi}\)
4 \(\frac{\mathrm{L}}{3 \pi}\)
Rotational Motion

149680 Figure shows triangular lamina which can rotate about different axis of rotation. Moment of inertia is maximum about the axis

1 QR
2 PR
3 QS
4 PQ
Rotational Motion

149676 Two particles of mass \(5 \mathrm{~kg}\) and \(10 \quad \mathrm{~kg}\) respectively are attached to the two ends of a rigid rod of length \(1 \mathrm{~m}\) with negligible mass. The centre of mass of the system from the \(5 \mathbf{~ k g}\) particle is nearly at a distance of

1 \(50 \mathrm{~cm}\)
2 \(67 \mathrm{~cm}\)
3 \(80 \mathrm{~cm}\)
4 \(33 \mathrm{~cm}\)
Rotational Motion

149677 Three identical spheres, each of mass \(M\), are placed at the corners of a right angle triangle with the mutually perpendicular sides equal to \(2 \mathrm{~m}\) (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of centre of mass.

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

149681 Consider a two block system having masses \(M_{A}=3 \mathrm{~kg}\) and \(M_{B}=\mathbf{2 k g}\), as shown in the figure. If block \(A\) is pushed towards the centre of mass through a distance \(200 \mathrm{~cm}\), by what distance should the block \(B\) be moved so as to keep the centre of mass at the same position.

1 \(200 \mathrm{~cm}\)
2 \(300 \mathrm{~cm}\)
3 \(130 \mathrm{~cm}\)
4 \(250 \mathrm{~cm}\)
Rotational Motion

149682 A uniform wire of length ' \(L\) ' with centre of mass at the origin is lying along the \(x\)-axis. The wire is bent in the form of a circle such that its lowest point is at the origin. Then shift of centre of mass is

1 \(\frac{L}{\pi}\)
2 \(\frac{2 \mathrm{~L}}{\pi}\)
3 \(\frac{\mathrm{L}}{2 \pi}\)
4 \(\frac{\mathrm{L}}{3 \pi}\)
Rotational Motion

149680 Figure shows triangular lamina which can rotate about different axis of rotation. Moment of inertia is maximum about the axis

1 QR
2 PR
3 QS
4 PQ