00. Centre of Mass
Rotational Motion

269360 Four particles, each of mass\(1 \mathrm{~kg}\) are placed at the corners of a square OABC of side \(1 \mathrm{~m}\). ' \(O\) ' is at the origin of the coordinate system. \(O A\) and \(O C\) are aligned along positive \(X\)-axis and positive \(Y\)-axis respectively. The position vector of the centre of mass is (in ' \(m\) ')

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

269361 A thick straight wire of length\(\pi m\) is fixed at its midpoint and then bent in the form of a circle. The shift in its centre of mass is

1 \(\pi m\)
2 \(0.5 \mathrm{~m}\)
3 \(2 \mathrm{~m}\)
4 \(\frac{\pi}{2} m\)
Rotational Motion

269362 A rigid body consists of a \(3 \mathrm{~kg}\) mass located at \(\vec{r}_{1}=(2 \hat{i}+5 \hat{j}) \mathrm{m}\) and a \(2 \mathrm{~kg}\) mass located at \(\vec{r}_{2}=(4 \hat{i}+2 \hat{j}) \mathbf{m}\). The position of centre of mass is

1 \(\square \frac{14}{5} \hat{\mathrm{j}}+\frac{19}{5} \hat{\mathrm{i}} \exists^{m}\)
2 \(\square \frac{14}{5} \hat{i}+\frac{19}{5} \hat{j} \square^{m}\)
3 \(\square \frac{19}{5} \hat{\mathrm{i}}+\frac{14}{5} \hat{j} \square^{m}\)
4 0
Rotational Motion

269363 A boat of mass\(40 \mathrm{~kg}\) is at rest. A dog of mass \(4 \mathrm{~kg}\) moves in the boat with a velocity of \(10 \mathrm{~m} / \mathrm{s}\). What is the velocity of boat(nearly)?

1 \(4 \mathrm{~m} / \mathrm{s}\)
2 \(2 \mathrm{~m} / \mathrm{s}\)
3 \(8 \mathrm{~m} / \mathrm{s}\)
4 \(1 \mathrm{~m} / \mathrm{s}\)
Rotational Motion

269360 Four particles, each of mass\(1 \mathrm{~kg}\) are placed at the corners of a square OABC of side \(1 \mathrm{~m}\). ' \(O\) ' is at the origin of the coordinate system. \(O A\) and \(O C\) are aligned along positive \(X\)-axis and positive \(Y\)-axis respectively. The position vector of the centre of mass is (in ' \(m\) ')

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

269361 A thick straight wire of length\(\pi m\) is fixed at its midpoint and then bent in the form of a circle. The shift in its centre of mass is

1 \(\pi m\)
2 \(0.5 \mathrm{~m}\)
3 \(2 \mathrm{~m}\)
4 \(\frac{\pi}{2} m\)
Rotational Motion

269362 A rigid body consists of a \(3 \mathrm{~kg}\) mass located at \(\vec{r}_{1}=(2 \hat{i}+5 \hat{j}) \mathrm{m}\) and a \(2 \mathrm{~kg}\) mass located at \(\vec{r}_{2}=(4 \hat{i}+2 \hat{j}) \mathbf{m}\). The position of centre of mass is

1 \(\square \frac{14}{5} \hat{\mathrm{j}}+\frac{19}{5} \hat{\mathrm{i}} \exists^{m}\)
2 \(\square \frac{14}{5} \hat{i}+\frac{19}{5} \hat{j} \square^{m}\)
3 \(\square \frac{19}{5} \hat{\mathrm{i}}+\frac{14}{5} \hat{j} \square^{m}\)
4 0
Rotational Motion

269363 A boat of mass\(40 \mathrm{~kg}\) is at rest. A dog of mass \(4 \mathrm{~kg}\) moves in the boat with a velocity of \(10 \mathrm{~m} / \mathrm{s}\). What is the velocity of boat(nearly)?

1 \(4 \mathrm{~m} / \mathrm{s}\)
2 \(2 \mathrm{~m} / \mathrm{s}\)
3 \(8 \mathrm{~m} / \mathrm{s}\)
4 \(1 \mathrm{~m} / \mathrm{s}\)
Rotational Motion

269360 Four particles, each of mass\(1 \mathrm{~kg}\) are placed at the corners of a square OABC of side \(1 \mathrm{~m}\). ' \(O\) ' is at the origin of the coordinate system. \(O A\) and \(O C\) are aligned along positive \(X\)-axis and positive \(Y\)-axis respectively. The position vector of the centre of mass is (in ' \(m\) ')

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

269361 A thick straight wire of length\(\pi m\) is fixed at its midpoint and then bent in the form of a circle. The shift in its centre of mass is

1 \(\pi m\)
2 \(0.5 \mathrm{~m}\)
3 \(2 \mathrm{~m}\)
4 \(\frac{\pi}{2} m\)
Rotational Motion

269362 A rigid body consists of a \(3 \mathrm{~kg}\) mass located at \(\vec{r}_{1}=(2 \hat{i}+5 \hat{j}) \mathrm{m}\) and a \(2 \mathrm{~kg}\) mass located at \(\vec{r}_{2}=(4 \hat{i}+2 \hat{j}) \mathbf{m}\). The position of centre of mass is

1 \(\square \frac{14}{5} \hat{\mathrm{j}}+\frac{19}{5} \hat{\mathrm{i}} \exists^{m}\)
2 \(\square \frac{14}{5} \hat{i}+\frac{19}{5} \hat{j} \square^{m}\)
3 \(\square \frac{19}{5} \hat{\mathrm{i}}+\frac{14}{5} \hat{j} \square^{m}\)
4 0
Rotational Motion

269363 A boat of mass\(40 \mathrm{~kg}\) is at rest. A dog of mass \(4 \mathrm{~kg}\) moves in the boat with a velocity of \(10 \mathrm{~m} / \mathrm{s}\). What is the velocity of boat(nearly)?

1 \(4 \mathrm{~m} / \mathrm{s}\)
2 \(2 \mathrm{~m} / \mathrm{s}\)
3 \(8 \mathrm{~m} / \mathrm{s}\)
4 \(1 \mathrm{~m} / \mathrm{s}\)
Rotational Motion

269360 Four particles, each of mass\(1 \mathrm{~kg}\) are placed at the corners of a square OABC of side \(1 \mathrm{~m}\). ' \(O\) ' is at the origin of the coordinate system. \(O A\) and \(O C\) are aligned along positive \(X\)-axis and positive \(Y\)-axis respectively. The position vector of the centre of mass is (in ' \(m\) ')

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

269361 A thick straight wire of length\(\pi m\) is fixed at its midpoint and then bent in the form of a circle. The shift in its centre of mass is

1 \(\pi m\)
2 \(0.5 \mathrm{~m}\)
3 \(2 \mathrm{~m}\)
4 \(\frac{\pi}{2} m\)
Rotational Motion

269362 A rigid body consists of a \(3 \mathrm{~kg}\) mass located at \(\vec{r}_{1}=(2 \hat{i}+5 \hat{j}) \mathrm{m}\) and a \(2 \mathrm{~kg}\) mass located at \(\vec{r}_{2}=(4 \hat{i}+2 \hat{j}) \mathbf{m}\). The position of centre of mass is

1 \(\square \frac{14}{5} \hat{\mathrm{j}}+\frac{19}{5} \hat{\mathrm{i}} \exists^{m}\)
2 \(\square \frac{14}{5} \hat{i}+\frac{19}{5} \hat{j} \square^{m}\)
3 \(\square \frac{19}{5} \hat{\mathrm{i}}+\frac{14}{5} \hat{j} \square^{m}\)
4 0
Rotational Motion

269363 A boat of mass\(40 \mathrm{~kg}\) is at rest. A dog of mass \(4 \mathrm{~kg}\) moves in the boat with a velocity of \(10 \mathrm{~m} / \mathrm{s}\). What is the velocity of boat(nearly)?

1 \(4 \mathrm{~m} / \mathrm{s}\)
2 \(2 \mathrm{~m} / \mathrm{s}\)
3 \(8 \mathrm{~m} / \mathrm{s}\)
4 \(1 \mathrm{~m} / \mathrm{s}\)