00. Centre of Mass
Rotational Motion

149696 Figure shows a thin rectangular copper plate with its centre of mass at origin \(O\) and side \(A B\) \(=2 \mathrm{BC}=2 \mathrm{~m}\).
If a quarter part of the plate (shown as shaded is removed, the centre of mass of the remaining plate would lie at)

1 \(\frac{1}{12} \mathrm{~m}, \frac{1}{6} \mathrm{~m}\)
2 \(\frac{1}{6} \mathrm{~m}, \frac{1}{12} \mathrm{~m}\)
3 \(\frac{1}{3} \mathrm{~m}, \frac{1}{6} \mathrm{~m}\)
4 \(\frac{1}{3} \mathrm{~m}, \frac{1}{2} \mathrm{~m}\)
Rotational Motion

149698 What is the distance of centre of mass of a half ring from centre if the ring has radius \(=0.5 \mathrm{~m}\) ?

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

149700 Two particles of masses in the ratio \(1: 2\) are placed along a vertical line. The lighter particle is raised through a height of \(9 \mathrm{~cm}\). To raise the centre of mass of the system by \(2 \mathrm{~cm}\), the heavier particle should be

1 Moved \(1.5 \mathrm{~cm}\) downward
2 Moved \(2 \mathrm{~cm}\) upward
3 Moved \(1.5 \mathrm{~cm}\) upward
4 Moved \(2 \mathrm{~cm}\) downward
Rotational Motion

149701 A \(30 \mathrm{~kg}\) boy stands at the far edge of a floating plank, whose near edge is against the shore of a river. The plank is \(10 \mathrm{~m}\) long and weighs \(10 \mathrm{~kg}\). If the boy walks to the near edge of the plank, how far from the shore does the plank move

1 \(7 \mathrm{~m}\)
2 \(8 \mathrm{~m}\)
3 \(7.5 \mathrm{~m}\)
4 \(15 \mathrm{~m}\)
Rotational Motion

149702 The masses and positions (in rectangular coordinates) of four particles are as follows: \(1 \mathrm{~kg}\) at \((\mathrm{a}, \mathrm{a}), 2 \mathrm{~kg}\) at \((-\mathrm{a}, \mathrm{a}), 3 \mathrm{~kg}\) at \((-\mathrm{a},-\mathrm{a})\) and \(4 \mathrm{~kg}\) at \((\mathrm{a},-\mathrm{a})\). The position vector of the centre of mass of the system of four particles is

1 \(-4 a \hat{i}\)
2 \(-4 a \hat{i}-4 a \hat{j}\)
3 0
4 \(-0.4 \mathrm{aj}\)
Rotational Motion

149696 Figure shows a thin rectangular copper plate with its centre of mass at origin \(O\) and side \(A B\) \(=2 \mathrm{BC}=2 \mathrm{~m}\).
If a quarter part of the plate (shown as shaded is removed, the centre of mass of the remaining plate would lie at)

1 \(\frac{1}{12} \mathrm{~m}, \frac{1}{6} \mathrm{~m}\)
2 \(\frac{1}{6} \mathrm{~m}, \frac{1}{12} \mathrm{~m}\)
3 \(\frac{1}{3} \mathrm{~m}, \frac{1}{6} \mathrm{~m}\)
4 \(\frac{1}{3} \mathrm{~m}, \frac{1}{2} \mathrm{~m}\)
Rotational Motion

149698 What is the distance of centre of mass of a half ring from centre if the ring has radius \(=0.5 \mathrm{~m}\) ?

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

149700 Two particles of masses in the ratio \(1: 2\) are placed along a vertical line. The lighter particle is raised through a height of \(9 \mathrm{~cm}\). To raise the centre of mass of the system by \(2 \mathrm{~cm}\), the heavier particle should be

1 Moved \(1.5 \mathrm{~cm}\) downward
2 Moved \(2 \mathrm{~cm}\) upward
3 Moved \(1.5 \mathrm{~cm}\) upward
4 Moved \(2 \mathrm{~cm}\) downward
Rotational Motion

149701 A \(30 \mathrm{~kg}\) boy stands at the far edge of a floating plank, whose near edge is against the shore of a river. The plank is \(10 \mathrm{~m}\) long and weighs \(10 \mathrm{~kg}\). If the boy walks to the near edge of the plank, how far from the shore does the plank move

1 \(7 \mathrm{~m}\)
2 \(8 \mathrm{~m}\)
3 \(7.5 \mathrm{~m}\)
4 \(15 \mathrm{~m}\)
Rotational Motion

149702 The masses and positions (in rectangular coordinates) of four particles are as follows: \(1 \mathrm{~kg}\) at \((\mathrm{a}, \mathrm{a}), 2 \mathrm{~kg}\) at \((-\mathrm{a}, \mathrm{a}), 3 \mathrm{~kg}\) at \((-\mathrm{a},-\mathrm{a})\) and \(4 \mathrm{~kg}\) at \((\mathrm{a},-\mathrm{a})\). The position vector of the centre of mass of the system of four particles is

1 \(-4 a \hat{i}\)
2 \(-4 a \hat{i}-4 a \hat{j}\)
3 0
4 \(-0.4 \mathrm{aj}\)
Rotational Motion

149696 Figure shows a thin rectangular copper plate with its centre of mass at origin \(O\) and side \(A B\) \(=2 \mathrm{BC}=2 \mathrm{~m}\).
If a quarter part of the plate (shown as shaded is removed, the centre of mass of the remaining plate would lie at)

1 \(\frac{1}{12} \mathrm{~m}, \frac{1}{6} \mathrm{~m}\)
2 \(\frac{1}{6} \mathrm{~m}, \frac{1}{12} \mathrm{~m}\)
3 \(\frac{1}{3} \mathrm{~m}, \frac{1}{6} \mathrm{~m}\)
4 \(\frac{1}{3} \mathrm{~m}, \frac{1}{2} \mathrm{~m}\)
Rotational Motion

149698 What is the distance of centre of mass of a half ring from centre if the ring has radius \(=0.5 \mathrm{~m}\) ?

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

149700 Two particles of masses in the ratio \(1: 2\) are placed along a vertical line. The lighter particle is raised through a height of \(9 \mathrm{~cm}\). To raise the centre of mass of the system by \(2 \mathrm{~cm}\), the heavier particle should be

1 Moved \(1.5 \mathrm{~cm}\) downward
2 Moved \(2 \mathrm{~cm}\) upward
3 Moved \(1.5 \mathrm{~cm}\) upward
4 Moved \(2 \mathrm{~cm}\) downward
Rotational Motion

149701 A \(30 \mathrm{~kg}\) boy stands at the far edge of a floating plank, whose near edge is against the shore of a river. The plank is \(10 \mathrm{~m}\) long and weighs \(10 \mathrm{~kg}\). If the boy walks to the near edge of the plank, how far from the shore does the plank move

1 \(7 \mathrm{~m}\)
2 \(8 \mathrm{~m}\)
3 \(7.5 \mathrm{~m}\)
4 \(15 \mathrm{~m}\)
Rotational Motion

149702 The masses and positions (in rectangular coordinates) of four particles are as follows: \(1 \mathrm{~kg}\) at \((\mathrm{a}, \mathrm{a}), 2 \mathrm{~kg}\) at \((-\mathrm{a}, \mathrm{a}), 3 \mathrm{~kg}\) at \((-\mathrm{a},-\mathrm{a})\) and \(4 \mathrm{~kg}\) at \((\mathrm{a},-\mathrm{a})\). The position vector of the centre of mass of the system of four particles is

1 \(-4 a \hat{i}\)
2 \(-4 a \hat{i}-4 a \hat{j}\)
3 0
4 \(-0.4 \mathrm{aj}\)
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Rotational Motion

149696 Figure shows a thin rectangular copper plate with its centre of mass at origin \(O\) and side \(A B\) \(=2 \mathrm{BC}=2 \mathrm{~m}\).
If a quarter part of the plate (shown as shaded is removed, the centre of mass of the remaining plate would lie at)

1 \(\frac{1}{12} \mathrm{~m}, \frac{1}{6} \mathrm{~m}\)
2 \(\frac{1}{6} \mathrm{~m}, \frac{1}{12} \mathrm{~m}\)
3 \(\frac{1}{3} \mathrm{~m}, \frac{1}{6} \mathrm{~m}\)
4 \(\frac{1}{3} \mathrm{~m}, \frac{1}{2} \mathrm{~m}\)
Rotational Motion

149698 What is the distance of centre of mass of a half ring from centre if the ring has radius \(=0.5 \mathrm{~m}\) ?

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

149700 Two particles of masses in the ratio \(1: 2\) are placed along a vertical line. The lighter particle is raised through a height of \(9 \mathrm{~cm}\). To raise the centre of mass of the system by \(2 \mathrm{~cm}\), the heavier particle should be

1 Moved \(1.5 \mathrm{~cm}\) downward
2 Moved \(2 \mathrm{~cm}\) upward
3 Moved \(1.5 \mathrm{~cm}\) upward
4 Moved \(2 \mathrm{~cm}\) downward
Rotational Motion

149701 A \(30 \mathrm{~kg}\) boy stands at the far edge of a floating plank, whose near edge is against the shore of a river. The plank is \(10 \mathrm{~m}\) long and weighs \(10 \mathrm{~kg}\). If the boy walks to the near edge of the plank, how far from the shore does the plank move

1 \(7 \mathrm{~m}\)
2 \(8 \mathrm{~m}\)
3 \(7.5 \mathrm{~m}\)
4 \(15 \mathrm{~m}\)
Rotational Motion

149702 The masses and positions (in rectangular coordinates) of four particles are as follows: \(1 \mathrm{~kg}\) at \((\mathrm{a}, \mathrm{a}), 2 \mathrm{~kg}\) at \((-\mathrm{a}, \mathrm{a}), 3 \mathrm{~kg}\) at \((-\mathrm{a},-\mathrm{a})\) and \(4 \mathrm{~kg}\) at \((\mathrm{a},-\mathrm{a})\). The position vector of the centre of mass of the system of four particles is

1 \(-4 a \hat{i}\)
2 \(-4 a \hat{i}-4 a \hat{j}\)
3 0
4 \(-0.4 \mathrm{aj}\)
Rotational Motion

149696 Figure shows a thin rectangular copper plate with its centre of mass at origin \(O\) and side \(A B\) \(=2 \mathrm{BC}=2 \mathrm{~m}\).
If a quarter part of the plate (shown as shaded is removed, the centre of mass of the remaining plate would lie at)

1 \(\frac{1}{12} \mathrm{~m}, \frac{1}{6} \mathrm{~m}\)
2 \(\frac{1}{6} \mathrm{~m}, \frac{1}{12} \mathrm{~m}\)
3 \(\frac{1}{3} \mathrm{~m}, \frac{1}{6} \mathrm{~m}\)
4 \(\frac{1}{3} \mathrm{~m}, \frac{1}{2} \mathrm{~m}\)
Rotational Motion

149698 What is the distance of centre of mass of a half ring from centre if the ring has radius \(=0.5 \mathrm{~m}\) ?

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

149700 Two particles of masses in the ratio \(1: 2\) are placed along a vertical line. The lighter particle is raised through a height of \(9 \mathrm{~cm}\). To raise the centre of mass of the system by \(2 \mathrm{~cm}\), the heavier particle should be

1 Moved \(1.5 \mathrm{~cm}\) downward
2 Moved \(2 \mathrm{~cm}\) upward
3 Moved \(1.5 \mathrm{~cm}\) upward
4 Moved \(2 \mathrm{~cm}\) downward
Rotational Motion

149701 A \(30 \mathrm{~kg}\) boy stands at the far edge of a floating plank, whose near edge is against the shore of a river. The plank is \(10 \mathrm{~m}\) long and weighs \(10 \mathrm{~kg}\). If the boy walks to the near edge of the plank, how far from the shore does the plank move

1 \(7 \mathrm{~m}\)
2 \(8 \mathrm{~m}\)
3 \(7.5 \mathrm{~m}\)
4 \(15 \mathrm{~m}\)
Rotational Motion

149702 The masses and positions (in rectangular coordinates) of four particles are as follows: \(1 \mathrm{~kg}\) at \((\mathrm{a}, \mathrm{a}), 2 \mathrm{~kg}\) at \((-\mathrm{a}, \mathrm{a}), 3 \mathrm{~kg}\) at \((-\mathrm{a},-\mathrm{a})\) and \(4 \mathrm{~kg}\) at \((\mathrm{a},-\mathrm{a})\). The position vector of the centre of mass of the system of four particles is

1 \(-4 a \hat{i}\)
2 \(-4 a \hat{i}-4 a \hat{j}\)
3 0
4 \(-0.4 \mathrm{aj}\)