Centre of Mass
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365728 Four particles of mass \({m_{1}=3 m, m_{2}=4 m}\) \({m_{3}=3 m}\), and \({m_{4}}\) are placed at four corners of a square. What should be the value of \({m_{4}}\) so that the centre of mass of all the four particles are exactly at the centre of the square?
supporting img

1 \({2 m}\)
2 \({8 m}\)
3 \({6 m}\)
4 \({4 m}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365729 Consider a two particle system with particles having masses \(m_{1}\) and \(m_{2}\). If the first particle is pushed towards the centre of mass through a distance \(d\), by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

1 \(\dfrac{m_{1}}{m_{1}+m_{2}} d\)
2 \(\dfrac{m_{2}}{m_{1}} d\)
3 \(d\)
4 \(\dfrac{m_{1}}{m_{2}} d\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365730 Three point particles of masses \(1.0 \mathrm{~kg}, 1.5 \mathrm{~kg}\) and \(2.5 \mathrm{~kg}\) are placed at three corners of a right angle triangle of sides \(4.0 \mathrm{~cm}, 3.0 \mathrm{~cm}\) and 5.0 \(\mathrm{cm}\) as shown in the figure. The center of mass of the system is at a point
supporting img

1 \(1.5 \mathrm{~cm}\) right and \(1.2 \mathrm{~cm}\) above \(1 \mathrm{~kg}\) mass
2 \(2.0 \mathrm{~cm}\) right and \(0.9 \mathrm{~cm}\) above \(1 \mathrm{~kg}\) mass
3 \(0.9 \mathrm{~cm}\) right and \(2.0 \mathrm{~cm}\) above \(1 \mathrm{~kg}\) mass
4 \(0.6 \mathrm{~cm}\) right and \(2.0 \mathrm{~cm}\) above \(1 \mathrm{~kg}\) mass
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365731 Three particles each of mass \(2\;kg\) are at the corners of an equilateral triangle of side \(\sqrt 3 \;m\). If the one of the particles is removed, the shift in the centre of mass is

1 \(0.2\;m\)
2 \(0.5\;m\)
3 \(0.4\;m\)
4 \(0.3\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365728 Four particles of mass \({m_{1}=3 m, m_{2}=4 m}\) \({m_{3}=3 m}\), and \({m_{4}}\) are placed at four corners of a square. What should be the value of \({m_{4}}\) so that the centre of mass of all the four particles are exactly at the centre of the square?
supporting img

1 \({2 m}\)
2 \({8 m}\)
3 \({6 m}\)
4 \({4 m}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365729 Consider a two particle system with particles having masses \(m_{1}\) and \(m_{2}\). If the first particle is pushed towards the centre of mass through a distance \(d\), by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

1 \(\dfrac{m_{1}}{m_{1}+m_{2}} d\)
2 \(\dfrac{m_{2}}{m_{1}} d\)
3 \(d\)
4 \(\dfrac{m_{1}}{m_{2}} d\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365730 Three point particles of masses \(1.0 \mathrm{~kg}, 1.5 \mathrm{~kg}\) and \(2.5 \mathrm{~kg}\) are placed at three corners of a right angle triangle of sides \(4.0 \mathrm{~cm}, 3.0 \mathrm{~cm}\) and 5.0 \(\mathrm{cm}\) as shown in the figure. The center of mass of the system is at a point
supporting img

1 \(1.5 \mathrm{~cm}\) right and \(1.2 \mathrm{~cm}\) above \(1 \mathrm{~kg}\) mass
2 \(2.0 \mathrm{~cm}\) right and \(0.9 \mathrm{~cm}\) above \(1 \mathrm{~kg}\) mass
3 \(0.9 \mathrm{~cm}\) right and \(2.0 \mathrm{~cm}\) above \(1 \mathrm{~kg}\) mass
4 \(0.6 \mathrm{~cm}\) right and \(2.0 \mathrm{~cm}\) above \(1 \mathrm{~kg}\) mass
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365731 Three particles each of mass \(2\;kg\) are at the corners of an equilateral triangle of side \(\sqrt 3 \;m\). If the one of the particles is removed, the shift in the centre of mass is

1 \(0.2\;m\)
2 \(0.5\;m\)
3 \(0.4\;m\)
4 \(0.3\;m\)
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365728 Four particles of mass \({m_{1}=3 m, m_{2}=4 m}\) \({m_{3}=3 m}\), and \({m_{4}}\) are placed at four corners of a square. What should be the value of \({m_{4}}\) so that the centre of mass of all the four particles are exactly at the centre of the square?
supporting img

1 \({2 m}\)
2 \({8 m}\)
3 \({6 m}\)
4 \({4 m}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365729 Consider a two particle system with particles having masses \(m_{1}\) and \(m_{2}\). If the first particle is pushed towards the centre of mass through a distance \(d\), by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

1 \(\dfrac{m_{1}}{m_{1}+m_{2}} d\)
2 \(\dfrac{m_{2}}{m_{1}} d\)
3 \(d\)
4 \(\dfrac{m_{1}}{m_{2}} d\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365730 Three point particles of masses \(1.0 \mathrm{~kg}, 1.5 \mathrm{~kg}\) and \(2.5 \mathrm{~kg}\) are placed at three corners of a right angle triangle of sides \(4.0 \mathrm{~cm}, 3.0 \mathrm{~cm}\) and 5.0 \(\mathrm{cm}\) as shown in the figure. The center of mass of the system is at a point
supporting img

1 \(1.5 \mathrm{~cm}\) right and \(1.2 \mathrm{~cm}\) above \(1 \mathrm{~kg}\) mass
2 \(2.0 \mathrm{~cm}\) right and \(0.9 \mathrm{~cm}\) above \(1 \mathrm{~kg}\) mass
3 \(0.9 \mathrm{~cm}\) right and \(2.0 \mathrm{~cm}\) above \(1 \mathrm{~kg}\) mass
4 \(0.6 \mathrm{~cm}\) right and \(2.0 \mathrm{~cm}\) above \(1 \mathrm{~kg}\) mass
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365731 Three particles each of mass \(2\;kg\) are at the corners of an equilateral triangle of side \(\sqrt 3 \;m\). If the one of the particles is removed, the shift in the centre of mass is

1 \(0.2\;m\)
2 \(0.5\;m\)
3 \(0.4\;m\)
4 \(0.3\;m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365728 Four particles of mass \({m_{1}=3 m, m_{2}=4 m}\) \({m_{3}=3 m}\), and \({m_{4}}\) are placed at four corners of a square. What should be the value of \({m_{4}}\) so that the centre of mass of all the four particles are exactly at the centre of the square?
supporting img

1 \({2 m}\)
2 \({8 m}\)
3 \({6 m}\)
4 \({4 m}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365729 Consider a two particle system with particles having masses \(m_{1}\) and \(m_{2}\). If the first particle is pushed towards the centre of mass through a distance \(d\), by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

1 \(\dfrac{m_{1}}{m_{1}+m_{2}} d\)
2 \(\dfrac{m_{2}}{m_{1}} d\)
3 \(d\)
4 \(\dfrac{m_{1}}{m_{2}} d\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365730 Three point particles of masses \(1.0 \mathrm{~kg}, 1.5 \mathrm{~kg}\) and \(2.5 \mathrm{~kg}\) are placed at three corners of a right angle triangle of sides \(4.0 \mathrm{~cm}, 3.0 \mathrm{~cm}\) and 5.0 \(\mathrm{cm}\) as shown in the figure. The center of mass of the system is at a point
supporting img

1 \(1.5 \mathrm{~cm}\) right and \(1.2 \mathrm{~cm}\) above \(1 \mathrm{~kg}\) mass
2 \(2.0 \mathrm{~cm}\) right and \(0.9 \mathrm{~cm}\) above \(1 \mathrm{~kg}\) mass
3 \(0.9 \mathrm{~cm}\) right and \(2.0 \mathrm{~cm}\) above \(1 \mathrm{~kg}\) mass
4 \(0.6 \mathrm{~cm}\) right and \(2.0 \mathrm{~cm}\) above \(1 \mathrm{~kg}\) mass
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365731 Three particles each of mass \(2\;kg\) are at the corners of an equilateral triangle of side \(\sqrt 3 \;m\). If the one of the particles is removed, the shift in the centre of mass is

1 \(0.2\;m\)
2 \(0.5\;m\)
3 \(0.4\;m\)
4 \(0.3\;m\)