Centre of Mass
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365775 A boy of mass \(m\) is standing on a block of mass \(M\) kept on a rough surface. When the boy walks from left to right on the block, the centre of mass (boy+block) of system:

1 Shifts towards left
2 Remains stationary
3 Shifts towards right if \(M>m\) and towards left if \(M < m.\)
4 Shift towards right.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365776 Two persons \(60\;kg\) and \(80\;kg\) are sitting at the ends of a boat of mass \(60\;kg\) and length \(4\;m\). The boat is stationary. If the men now exchange their positions, then:

1 The boat moves by \(0.4 \mathrm{~m}\)
2 The boat moves by \(0.6\;m\)
3 The centre of mass of the two men shifts by \(2\;m\)
4 The centre of mass of the two men shifts by \(\frac{4}{7}m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365777 The centre of mass of three particles of mass \(1\;kg,2\;kg\) and \(3\;kg\) is at \((3,3,3)\) with reference to a fixed coordinate system. Where should be fourth particle of mass \(4\;kg\) be placed, so that the centre of mass of the system of all particles shifts to a point \((1,1,1)\) ?

1 \((-1,-1,-1)\)
2 \((-2,-2,-2)\)
3 \((2,2,2)\)
4 \((1,1,1)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365778 A wedge \(\mathrm{Q}\) of mass \(M\) is placed on a horizontal frictionless surface \(A B\) and a block \(P\) of mass \(m\) is released on its frictionless slope. As \(P\) slides by a length \(L\) on this slope of inclination \(\theta, \mathrm{Q}\) would slide by a distance of
supporting img

1 \(\dfrac{m}{L}(M+m)\)
2 \(\left(\dfrac{m}{L}\right)(M+m)\)
3 \(\dfrac{(m L \cos \theta)}{(m+M)}\)
4 \(\dfrac{(m+M)}{(m L \cos \theta)}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365775 A boy of mass \(m\) is standing on a block of mass \(M\) kept on a rough surface. When the boy walks from left to right on the block, the centre of mass (boy+block) of system:

1 Shifts towards left
2 Remains stationary
3 Shifts towards right if \(M>m\) and towards left if \(M < m.\)
4 Shift towards right.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365776 Two persons \(60\;kg\) and \(80\;kg\) are sitting at the ends of a boat of mass \(60\;kg\) and length \(4\;m\). The boat is stationary. If the men now exchange their positions, then:

1 The boat moves by \(0.4 \mathrm{~m}\)
2 The boat moves by \(0.6\;m\)
3 The centre of mass of the two men shifts by \(2\;m\)
4 The centre of mass of the two men shifts by \(\frac{4}{7}m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365777 The centre of mass of three particles of mass \(1\;kg,2\;kg\) and \(3\;kg\) is at \((3,3,3)\) with reference to a fixed coordinate system. Where should be fourth particle of mass \(4\;kg\) be placed, so that the centre of mass of the system of all particles shifts to a point \((1,1,1)\) ?

1 \((-1,-1,-1)\)
2 \((-2,-2,-2)\)
3 \((2,2,2)\)
4 \((1,1,1)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365778 A wedge \(\mathrm{Q}\) of mass \(M\) is placed on a horizontal frictionless surface \(A B\) and a block \(P\) of mass \(m\) is released on its frictionless slope. As \(P\) slides by a length \(L\) on this slope of inclination \(\theta, \mathrm{Q}\) would slide by a distance of
supporting img

1 \(\dfrac{m}{L}(M+m)\)
2 \(\left(\dfrac{m}{L}\right)(M+m)\)
3 \(\dfrac{(m L \cos \theta)}{(m+M)}\)
4 \(\dfrac{(m+M)}{(m L \cos \theta)}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365775 A boy of mass \(m\) is standing on a block of mass \(M\) kept on a rough surface. When the boy walks from left to right on the block, the centre of mass (boy+block) of system:

1 Shifts towards left
2 Remains stationary
3 Shifts towards right if \(M>m\) and towards left if \(M < m.\)
4 Shift towards right.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365776 Two persons \(60\;kg\) and \(80\;kg\) are sitting at the ends of a boat of mass \(60\;kg\) and length \(4\;m\). The boat is stationary. If the men now exchange their positions, then:

1 The boat moves by \(0.4 \mathrm{~m}\)
2 The boat moves by \(0.6\;m\)
3 The centre of mass of the two men shifts by \(2\;m\)
4 The centre of mass of the two men shifts by \(\frac{4}{7}m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365777 The centre of mass of three particles of mass \(1\;kg,2\;kg\) and \(3\;kg\) is at \((3,3,3)\) with reference to a fixed coordinate system. Where should be fourth particle of mass \(4\;kg\) be placed, so that the centre of mass of the system of all particles shifts to a point \((1,1,1)\) ?

1 \((-1,-1,-1)\)
2 \((-2,-2,-2)\)
3 \((2,2,2)\)
4 \((1,1,1)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365778 A wedge \(\mathrm{Q}\) of mass \(M\) is placed on a horizontal frictionless surface \(A B\) and a block \(P\) of mass \(m\) is released on its frictionless slope. As \(P\) slides by a length \(L\) on this slope of inclination \(\theta, \mathrm{Q}\) would slide by a distance of
supporting img

1 \(\dfrac{m}{L}(M+m)\)
2 \(\left(\dfrac{m}{L}\right)(M+m)\)
3 \(\dfrac{(m L \cos \theta)}{(m+M)}\)
4 \(\dfrac{(m+M)}{(m L \cos \theta)}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365775 A boy of mass \(m\) is standing on a block of mass \(M\) kept on a rough surface. When the boy walks from left to right on the block, the centre of mass (boy+block) of system:

1 Shifts towards left
2 Remains stationary
3 Shifts towards right if \(M>m\) and towards left if \(M < m.\)
4 Shift towards right.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365776 Two persons \(60\;kg\) and \(80\;kg\) are sitting at the ends of a boat of mass \(60\;kg\) and length \(4\;m\). The boat is stationary. If the men now exchange their positions, then:

1 The boat moves by \(0.4 \mathrm{~m}\)
2 The boat moves by \(0.6\;m\)
3 The centre of mass of the two men shifts by \(2\;m\)
4 The centre of mass of the two men shifts by \(\frac{4}{7}m\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365777 The centre of mass of three particles of mass \(1\;kg,2\;kg\) and \(3\;kg\) is at \((3,3,3)\) with reference to a fixed coordinate system. Where should be fourth particle of mass \(4\;kg\) be placed, so that the centre of mass of the system of all particles shifts to a point \((1,1,1)\) ?

1 \((-1,-1,-1)\)
2 \((-2,-2,-2)\)
3 \((2,2,2)\)
4 \((1,1,1)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365778 A wedge \(\mathrm{Q}\) of mass \(M\) is placed on a horizontal frictionless surface \(A B\) and a block \(P\) of mass \(m\) is released on its frictionless slope. As \(P\) slides by a length \(L\) on this slope of inclination \(\theta, \mathrm{Q}\) would slide by a distance of
supporting img

1 \(\dfrac{m}{L}(M+m)\)
2 \(\left(\dfrac{m}{L}\right)(M+m)\)
3 \(\dfrac{(m L \cos \theta)}{(m+M)}\)
4 \(\dfrac{(m+M)}{(m L \cos \theta)}\)