00. Centre of Mass
Rotational Motion

149665 Two blocks of masses \(10 \mathrm{~kg}\) and \(30 \mathrm{~kg}\) are placed on the same straight line with coordinates \((0,0) \mathrm{cm}\) and \((x, 0) \mathrm{cm}\) respectively. The block of \(10 \mathrm{~kg}\) is moved on the same line though a distance of \(6 \mathrm{~cm}\) towards the other block. The distance through which the block of \(30 \mathrm{~kg}\) must be moved to keep the position of centre of mass of the system unchanged is

1 \(4 \mathrm{~cm}\) towards the \(10 \mathrm{~kg}\) block
2 \(2 \mathrm{~cm}\) away from the \(10 \mathrm{~kg}\) block
3 \(2 \mathrm{~cm}\) towards the \(10 \mathrm{~kg}\) block
4 \(4 \mathrm{~cm}\) away from the \(10 \mathrm{~kg}\) block
Rotational Motion

149666 Four masses are arranged along a circle of radius \(1 \mathrm{~m}\) as shown in the figure. The center of mass of this system of masses is at

1 \(-\frac{1}{5} \hat{\mathrm{i}}-\frac{1}{5} \hat{\mathrm{j}}\)
2 \(\frac{1}{5} \hat{\mathrm{i}}+\hat{\mathrm{j}}\)
3 \(\hat{\mathrm{i}}-\frac{1}{5} \widehat{\mathrm{j}}\)
4 \(\frac{1}{5} \hat{\mathrm{i}}+\frac{1}{5} \hat{\mathrm{j}}\)
Rotational Motion

149667 A metre stick is balanced on a knife edge at its centre. When four coins, each of mass \(2 \mathrm{~g}\) are put one on top of the other at \(10.0 \mathrm{~cm}\) mark, the stick it found to be balanced at \(46.0 \mathrm{~cm}\) mark. The mass of the metre stick is

1 \(66 \mathrm{~g}\)
2 \(60 \mathrm{~g}\)
3 \(72 \mathrm{~g}\)
4 \(18 \mathrm{~g}\)
Rotational Motion

149669 A man weighing \(70 \mathrm{~kg}\) is riding on a cart of mass \(30 \mathrm{~kg}\) which moves along a level floor at a speed of \(3 \mathrm{~ms}^{-1}\). If he runs on the cart so that his velocity relative to the cart is \(4 \mathrm{~ms}^{-1}\) in the direction opposite to the motion of the cart, the speed of centre of mass of the system is

1 \(0.3 \mathrm{~ms}^{-1}\)
2 \(0.5 \mathrm{~ms}^{-1}\)
3 \(0.2 \mathrm{~ms}^{-1}\)
4 \(0.1 \mathrm{~ms}^{-1}\)
5 zero
Rotational Motion

149665 Two blocks of masses \(10 \mathrm{~kg}\) and \(30 \mathrm{~kg}\) are placed on the same straight line with coordinates \((0,0) \mathrm{cm}\) and \((x, 0) \mathrm{cm}\) respectively. The block of \(10 \mathrm{~kg}\) is moved on the same line though a distance of \(6 \mathrm{~cm}\) towards the other block. The distance through which the block of \(30 \mathrm{~kg}\) must be moved to keep the position of centre of mass of the system unchanged is

1 \(4 \mathrm{~cm}\) towards the \(10 \mathrm{~kg}\) block
2 \(2 \mathrm{~cm}\) away from the \(10 \mathrm{~kg}\) block
3 \(2 \mathrm{~cm}\) towards the \(10 \mathrm{~kg}\) block
4 \(4 \mathrm{~cm}\) away from the \(10 \mathrm{~kg}\) block
Rotational Motion

149666 Four masses are arranged along a circle of radius \(1 \mathrm{~m}\) as shown in the figure. The center of mass of this system of masses is at

1 \(-\frac{1}{5} \hat{\mathrm{i}}-\frac{1}{5} \hat{\mathrm{j}}\)
2 \(\frac{1}{5} \hat{\mathrm{i}}+\hat{\mathrm{j}}\)
3 \(\hat{\mathrm{i}}-\frac{1}{5} \widehat{\mathrm{j}}\)
4 \(\frac{1}{5} \hat{\mathrm{i}}+\frac{1}{5} \hat{\mathrm{j}}\)
Rotational Motion

149667 A metre stick is balanced on a knife edge at its centre. When four coins, each of mass \(2 \mathrm{~g}\) are put one on top of the other at \(10.0 \mathrm{~cm}\) mark, the stick it found to be balanced at \(46.0 \mathrm{~cm}\) mark. The mass of the metre stick is

1 \(66 \mathrm{~g}\)
2 \(60 \mathrm{~g}\)
3 \(72 \mathrm{~g}\)
4 \(18 \mathrm{~g}\)
Rotational Motion

149669 A man weighing \(70 \mathrm{~kg}\) is riding on a cart of mass \(30 \mathrm{~kg}\) which moves along a level floor at a speed of \(3 \mathrm{~ms}^{-1}\). If he runs on the cart so that his velocity relative to the cart is \(4 \mathrm{~ms}^{-1}\) in the direction opposite to the motion of the cart, the speed of centre of mass of the system is

1 \(0.3 \mathrm{~ms}^{-1}\)
2 \(0.5 \mathrm{~ms}^{-1}\)
3 \(0.2 \mathrm{~ms}^{-1}\)
4 \(0.1 \mathrm{~ms}^{-1}\)
5 zero
Rotational Motion

149665 Two blocks of masses \(10 \mathrm{~kg}\) and \(30 \mathrm{~kg}\) are placed on the same straight line with coordinates \((0,0) \mathrm{cm}\) and \((x, 0) \mathrm{cm}\) respectively. The block of \(10 \mathrm{~kg}\) is moved on the same line though a distance of \(6 \mathrm{~cm}\) towards the other block. The distance through which the block of \(30 \mathrm{~kg}\) must be moved to keep the position of centre of mass of the system unchanged is

1 \(4 \mathrm{~cm}\) towards the \(10 \mathrm{~kg}\) block
2 \(2 \mathrm{~cm}\) away from the \(10 \mathrm{~kg}\) block
3 \(2 \mathrm{~cm}\) towards the \(10 \mathrm{~kg}\) block
4 \(4 \mathrm{~cm}\) away from the \(10 \mathrm{~kg}\) block
Rotational Motion

149666 Four masses are arranged along a circle of radius \(1 \mathrm{~m}\) as shown in the figure. The center of mass of this system of masses is at

1 \(-\frac{1}{5} \hat{\mathrm{i}}-\frac{1}{5} \hat{\mathrm{j}}\)
2 \(\frac{1}{5} \hat{\mathrm{i}}+\hat{\mathrm{j}}\)
3 \(\hat{\mathrm{i}}-\frac{1}{5} \widehat{\mathrm{j}}\)
4 \(\frac{1}{5} \hat{\mathrm{i}}+\frac{1}{5} \hat{\mathrm{j}}\)
Rotational Motion

149667 A metre stick is balanced on a knife edge at its centre. When four coins, each of mass \(2 \mathrm{~g}\) are put one on top of the other at \(10.0 \mathrm{~cm}\) mark, the stick it found to be balanced at \(46.0 \mathrm{~cm}\) mark. The mass of the metre stick is

1 \(66 \mathrm{~g}\)
2 \(60 \mathrm{~g}\)
3 \(72 \mathrm{~g}\)
4 \(18 \mathrm{~g}\)
Rotational Motion

149669 A man weighing \(70 \mathrm{~kg}\) is riding on a cart of mass \(30 \mathrm{~kg}\) which moves along a level floor at a speed of \(3 \mathrm{~ms}^{-1}\). If he runs on the cart so that his velocity relative to the cart is \(4 \mathrm{~ms}^{-1}\) in the direction opposite to the motion of the cart, the speed of centre of mass of the system is

1 \(0.3 \mathrm{~ms}^{-1}\)
2 \(0.5 \mathrm{~ms}^{-1}\)
3 \(0.2 \mathrm{~ms}^{-1}\)
4 \(0.1 \mathrm{~ms}^{-1}\)
5 zero
Rotational Motion

149665 Two blocks of masses \(10 \mathrm{~kg}\) and \(30 \mathrm{~kg}\) are placed on the same straight line with coordinates \((0,0) \mathrm{cm}\) and \((x, 0) \mathrm{cm}\) respectively. The block of \(10 \mathrm{~kg}\) is moved on the same line though a distance of \(6 \mathrm{~cm}\) towards the other block. The distance through which the block of \(30 \mathrm{~kg}\) must be moved to keep the position of centre of mass of the system unchanged is

1 \(4 \mathrm{~cm}\) towards the \(10 \mathrm{~kg}\) block
2 \(2 \mathrm{~cm}\) away from the \(10 \mathrm{~kg}\) block
3 \(2 \mathrm{~cm}\) towards the \(10 \mathrm{~kg}\) block
4 \(4 \mathrm{~cm}\) away from the \(10 \mathrm{~kg}\) block
Rotational Motion

149666 Four masses are arranged along a circle of radius \(1 \mathrm{~m}\) as shown in the figure. The center of mass of this system of masses is at

1 \(-\frac{1}{5} \hat{\mathrm{i}}-\frac{1}{5} \hat{\mathrm{j}}\)
2 \(\frac{1}{5} \hat{\mathrm{i}}+\hat{\mathrm{j}}\)
3 \(\hat{\mathrm{i}}-\frac{1}{5} \widehat{\mathrm{j}}\)
4 \(\frac{1}{5} \hat{\mathrm{i}}+\frac{1}{5} \hat{\mathrm{j}}\)
Rotational Motion

149667 A metre stick is balanced on a knife edge at its centre. When four coins, each of mass \(2 \mathrm{~g}\) are put one on top of the other at \(10.0 \mathrm{~cm}\) mark, the stick it found to be balanced at \(46.0 \mathrm{~cm}\) mark. The mass of the metre stick is

1 \(66 \mathrm{~g}\)
2 \(60 \mathrm{~g}\)
3 \(72 \mathrm{~g}\)
4 \(18 \mathrm{~g}\)
Rotational Motion

149669 A man weighing \(70 \mathrm{~kg}\) is riding on a cart of mass \(30 \mathrm{~kg}\) which moves along a level floor at a speed of \(3 \mathrm{~ms}^{-1}\). If he runs on the cart so that his velocity relative to the cart is \(4 \mathrm{~ms}^{-1}\) in the direction opposite to the motion of the cart, the speed of centre of mass of the system is

1 \(0.3 \mathrm{~ms}^{-1}\)
2 \(0.5 \mathrm{~ms}^{-1}\)
3 \(0.2 \mathrm{~ms}^{-1}\)
4 \(0.1 \mathrm{~ms}^{-1}\)
5 zero