365719
\(C M\) of the given system of particles will be at
1 OD
2 OC
3 OB
4 AO
Explanation:
If all the masses were same, the \(C M\) was at \(O\) but as the mass at \(B\) is \(2 m\), so the \(C M\) of the system will shift towards \(B\). So, \(C M\) will be on line \(O B\).
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365720
The centre of mass of two particles lies
1 On the line perpendicular to the line joining the particles
2 On a point outside the line joining the particles
3 On the line joining the particles
4 None of the above
Explanation:
Conceptual Question
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365721
Six identical particles each of mass ' \(m\) ' are arranged at the corners of a regular hexagon of side length " \(L\) ". If the mass of one of the particle is doubled, the shift in the centre of mass is
1 \(L\)
2 \(6 L / 7\)
3 \(L / 7\)
4 \(\dfrac{L}{\sqrt{3}}\)
Explanation:
Let the \(C O M\) initial be at the origin. When one of masses is double then the new location will be \(X=\dfrac{(6 m) 0+m L}{7 m}=\dfrac{L}{7} .\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365722
Four particles of masses \(m_{1}, m_{2}, m_{3}\) and \(m_{4}\) are placed at the vertices \(A,{\rm{ }}B,{\rm{ }}C\) and \(D\) respectively of a square shown. The \(COM\) of the system will lie at diagonal \(AC\) if
1 \(m_{2}=m_{4}\)
2 \(m_{1}=m_{3}\)
3 \(m_{3}=m_{4}\)
4 \(m_{1}=m_{2}\)
Explanation:
Conceptual Question
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365723
Two point masses \(M\) each are placed at \((L,0)\,\& \,( - L,0)\). A third point mass \(\mathrm{M}\) is uniformly rotating on the circle \(x^{2}+y^{2}=L^{2}\). Equation of path traced by COM of system is
1 \(x^{2}+y^{2}=L^{2}\)
2 \(x^{2}+y^{2}=L^{2} / 3\)
3 \(x=y=0\)
4 \(x^{2}+y^{2}=L^{2} / 9\)
Explanation:
The position of the rotating particle at some arbitrary position is shown in the figure. The \(C.M\) of the two fixed particles \(1\,\,\& \,\,2\) lies at the origin. The resultant \(C.M\) lies at a distance \(\dfrac{L}{3}\) from the centre which rotates in a circle of radius \(\dfrac{L}{3}\)
365719
\(C M\) of the given system of particles will be at
1 OD
2 OC
3 OB
4 AO
Explanation:
If all the masses were same, the \(C M\) was at \(O\) but as the mass at \(B\) is \(2 m\), so the \(C M\) of the system will shift towards \(B\). So, \(C M\) will be on line \(O B\).
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365720
The centre of mass of two particles lies
1 On the line perpendicular to the line joining the particles
2 On a point outside the line joining the particles
3 On the line joining the particles
4 None of the above
Explanation:
Conceptual Question
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365721
Six identical particles each of mass ' \(m\) ' are arranged at the corners of a regular hexagon of side length " \(L\) ". If the mass of one of the particle is doubled, the shift in the centre of mass is
1 \(L\)
2 \(6 L / 7\)
3 \(L / 7\)
4 \(\dfrac{L}{\sqrt{3}}\)
Explanation:
Let the \(C O M\) initial be at the origin. When one of masses is double then the new location will be \(X=\dfrac{(6 m) 0+m L}{7 m}=\dfrac{L}{7} .\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365722
Four particles of masses \(m_{1}, m_{2}, m_{3}\) and \(m_{4}\) are placed at the vertices \(A,{\rm{ }}B,{\rm{ }}C\) and \(D\) respectively of a square shown. The \(COM\) of the system will lie at diagonal \(AC\) if
1 \(m_{2}=m_{4}\)
2 \(m_{1}=m_{3}\)
3 \(m_{3}=m_{4}\)
4 \(m_{1}=m_{2}\)
Explanation:
Conceptual Question
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365723
Two point masses \(M\) each are placed at \((L,0)\,\& \,( - L,0)\). A third point mass \(\mathrm{M}\) is uniformly rotating on the circle \(x^{2}+y^{2}=L^{2}\). Equation of path traced by COM of system is
1 \(x^{2}+y^{2}=L^{2}\)
2 \(x^{2}+y^{2}=L^{2} / 3\)
3 \(x=y=0\)
4 \(x^{2}+y^{2}=L^{2} / 9\)
Explanation:
The position of the rotating particle at some arbitrary position is shown in the figure. The \(C.M\) of the two fixed particles \(1\,\,\& \,\,2\) lies at the origin. The resultant \(C.M\) lies at a distance \(\dfrac{L}{3}\) from the centre which rotates in a circle of radius \(\dfrac{L}{3}\)
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365719
\(C M\) of the given system of particles will be at
1 OD
2 OC
3 OB
4 AO
Explanation:
If all the masses were same, the \(C M\) was at \(O\) but as the mass at \(B\) is \(2 m\), so the \(C M\) of the system will shift towards \(B\). So, \(C M\) will be on line \(O B\).
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365720
The centre of mass of two particles lies
1 On the line perpendicular to the line joining the particles
2 On a point outside the line joining the particles
3 On the line joining the particles
4 None of the above
Explanation:
Conceptual Question
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365721
Six identical particles each of mass ' \(m\) ' are arranged at the corners of a regular hexagon of side length " \(L\) ". If the mass of one of the particle is doubled, the shift in the centre of mass is
1 \(L\)
2 \(6 L / 7\)
3 \(L / 7\)
4 \(\dfrac{L}{\sqrt{3}}\)
Explanation:
Let the \(C O M\) initial be at the origin. When one of masses is double then the new location will be \(X=\dfrac{(6 m) 0+m L}{7 m}=\dfrac{L}{7} .\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365722
Four particles of masses \(m_{1}, m_{2}, m_{3}\) and \(m_{4}\) are placed at the vertices \(A,{\rm{ }}B,{\rm{ }}C\) and \(D\) respectively of a square shown. The \(COM\) of the system will lie at diagonal \(AC\) if
1 \(m_{2}=m_{4}\)
2 \(m_{1}=m_{3}\)
3 \(m_{3}=m_{4}\)
4 \(m_{1}=m_{2}\)
Explanation:
Conceptual Question
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365723
Two point masses \(M\) each are placed at \((L,0)\,\& \,( - L,0)\). A third point mass \(\mathrm{M}\) is uniformly rotating on the circle \(x^{2}+y^{2}=L^{2}\). Equation of path traced by COM of system is
1 \(x^{2}+y^{2}=L^{2}\)
2 \(x^{2}+y^{2}=L^{2} / 3\)
3 \(x=y=0\)
4 \(x^{2}+y^{2}=L^{2} / 9\)
Explanation:
The position of the rotating particle at some arbitrary position is shown in the figure. The \(C.M\) of the two fixed particles \(1\,\,\& \,\,2\) lies at the origin. The resultant \(C.M\) lies at a distance \(\dfrac{L}{3}\) from the centre which rotates in a circle of radius \(\dfrac{L}{3}\)
365719
\(C M\) of the given system of particles will be at
1 OD
2 OC
3 OB
4 AO
Explanation:
If all the masses were same, the \(C M\) was at \(O\) but as the mass at \(B\) is \(2 m\), so the \(C M\) of the system will shift towards \(B\). So, \(C M\) will be on line \(O B\).
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365720
The centre of mass of two particles lies
1 On the line perpendicular to the line joining the particles
2 On a point outside the line joining the particles
3 On the line joining the particles
4 None of the above
Explanation:
Conceptual Question
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365721
Six identical particles each of mass ' \(m\) ' are arranged at the corners of a regular hexagon of side length " \(L\) ". If the mass of one of the particle is doubled, the shift in the centre of mass is
1 \(L\)
2 \(6 L / 7\)
3 \(L / 7\)
4 \(\dfrac{L}{\sqrt{3}}\)
Explanation:
Let the \(C O M\) initial be at the origin. When one of masses is double then the new location will be \(X=\dfrac{(6 m) 0+m L}{7 m}=\dfrac{L}{7} .\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365722
Four particles of masses \(m_{1}, m_{2}, m_{3}\) and \(m_{4}\) are placed at the vertices \(A,{\rm{ }}B,{\rm{ }}C\) and \(D\) respectively of a square shown. The \(COM\) of the system will lie at diagonal \(AC\) if
1 \(m_{2}=m_{4}\)
2 \(m_{1}=m_{3}\)
3 \(m_{3}=m_{4}\)
4 \(m_{1}=m_{2}\)
Explanation:
Conceptual Question
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365723
Two point masses \(M\) each are placed at \((L,0)\,\& \,( - L,0)\). A third point mass \(\mathrm{M}\) is uniformly rotating on the circle \(x^{2}+y^{2}=L^{2}\). Equation of path traced by COM of system is
1 \(x^{2}+y^{2}=L^{2}\)
2 \(x^{2}+y^{2}=L^{2} / 3\)
3 \(x=y=0\)
4 \(x^{2}+y^{2}=L^{2} / 9\)
Explanation:
The position of the rotating particle at some arbitrary position is shown in the figure. The \(C.M\) of the two fixed particles \(1\,\,\& \,\,2\) lies at the origin. The resultant \(C.M\) lies at a distance \(\dfrac{L}{3}\) from the centre which rotates in a circle of radius \(\dfrac{L}{3}\)
365719
\(C M\) of the given system of particles will be at
1 OD
2 OC
3 OB
4 AO
Explanation:
If all the masses were same, the \(C M\) was at \(O\) but as the mass at \(B\) is \(2 m\), so the \(C M\) of the system will shift towards \(B\). So, \(C M\) will be on line \(O B\).
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365720
The centre of mass of two particles lies
1 On the line perpendicular to the line joining the particles
2 On a point outside the line joining the particles
3 On the line joining the particles
4 None of the above
Explanation:
Conceptual Question
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365721
Six identical particles each of mass ' \(m\) ' are arranged at the corners of a regular hexagon of side length " \(L\) ". If the mass of one of the particle is doubled, the shift in the centre of mass is
1 \(L\)
2 \(6 L / 7\)
3 \(L / 7\)
4 \(\dfrac{L}{\sqrt{3}}\)
Explanation:
Let the \(C O M\) initial be at the origin. When one of masses is double then the new location will be \(X=\dfrac{(6 m) 0+m L}{7 m}=\dfrac{L}{7} .\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365722
Four particles of masses \(m_{1}, m_{2}, m_{3}\) and \(m_{4}\) are placed at the vertices \(A,{\rm{ }}B,{\rm{ }}C\) and \(D\) respectively of a square shown. The \(COM\) of the system will lie at diagonal \(AC\) if
1 \(m_{2}=m_{4}\)
2 \(m_{1}=m_{3}\)
3 \(m_{3}=m_{4}\)
4 \(m_{1}=m_{2}\)
Explanation:
Conceptual Question
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365723
Two point masses \(M\) each are placed at \((L,0)\,\& \,( - L,0)\). A third point mass \(\mathrm{M}\) is uniformly rotating on the circle \(x^{2}+y^{2}=L^{2}\). Equation of path traced by COM of system is
1 \(x^{2}+y^{2}=L^{2}\)
2 \(x^{2}+y^{2}=L^{2} / 3\)
3 \(x=y=0\)
4 \(x^{2}+y^{2}=L^{2} / 9\)
Explanation:
The position of the rotating particle at some arbitrary position is shown in the figure. The \(C.M\) of the two fixed particles \(1\,\,\& \,\,2\) lies at the origin. The resultant \(C.M\) lies at a distance \(\dfrac{L}{3}\) from the centre which rotates in a circle of radius \(\dfrac{L}{3}\)
