Centre of Mass
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365754 Five uniform circular plates, each of diameter \(D\) and mass \(m\) are laid out in a pattern shown. Using the origin shown, find the \(y\) co-ordinate of the centre of mass of the five-plate system.
supporting img

1 \(4 D / 5\)
2 \(2 D / 5\)
3 \(D / 5\)
4 \(D / 3\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365755 Two identical thin uniform rods of length \(L\) each are joined to form \(T\) shape as shown in the figure. The distance of centre of mass from \(D\) is
supporting img

1 0
2 \(L / 4\)
3 \(3 L / 4\)
4 \(L\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365756 Assertion :
The centre of mass of uniform triangular lamina is centroid.
Reason :
Centroid is centre of symmetry of mass of the triangular lamina.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365757 A thin bar of length \(L\) has a mass per unit length \(\lambda\), that increases linearly with distance from one end. If its total mass is \(\mathrm{M}\) and its mass per unit length at the lighter end is \(\lambda_{0}\), then the distance of the centre of mass from the lighter end is :-

1 \(\frac{{2\;L}}{3} - \frac{{{\lambda _0}\;{L^2}}}{{6M}}\)
2 \(\frac{L}{3} + \frac{{{\lambda _0}\;{L^2}}}{{8M}}\)
3 \(\frac{L}{2} - \frac{{{\lambda _0}{L^2}}}{{4M}}\)
4 \(\frac{L}{3} + \frac{{{\lambda _0}\;{L^2}}}{{4M}}\)
JEE - 2014
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365754 Five uniform circular plates, each of diameter \(D\) and mass \(m\) are laid out in a pattern shown. Using the origin shown, find the \(y\) co-ordinate of the centre of mass of the five-plate system.
supporting img

1 \(4 D / 5\)
2 \(2 D / 5\)
3 \(D / 5\)
4 \(D / 3\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365755 Two identical thin uniform rods of length \(L\) each are joined to form \(T\) shape as shown in the figure. The distance of centre of mass from \(D\) is
supporting img

1 0
2 \(L / 4\)
3 \(3 L / 4\)
4 \(L\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365756 Assertion :
The centre of mass of uniform triangular lamina is centroid.
Reason :
Centroid is centre of symmetry of mass of the triangular lamina.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365757 A thin bar of length \(L\) has a mass per unit length \(\lambda\), that increases linearly with distance from one end. If its total mass is \(\mathrm{M}\) and its mass per unit length at the lighter end is \(\lambda_{0}\), then the distance of the centre of mass from the lighter end is :-

1 \(\frac{{2\;L}}{3} - \frac{{{\lambda _0}\;{L^2}}}{{6M}}\)
2 \(\frac{L}{3} + \frac{{{\lambda _0}\;{L^2}}}{{8M}}\)
3 \(\frac{L}{2} - \frac{{{\lambda _0}{L^2}}}{{4M}}\)
4 \(\frac{L}{3} + \frac{{{\lambda _0}\;{L^2}}}{{4M}}\)
JEE - 2014
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365754 Five uniform circular plates, each of diameter \(D\) and mass \(m\) are laid out in a pattern shown. Using the origin shown, find the \(y\) co-ordinate of the centre of mass of the five-plate system.
supporting img

1 \(4 D / 5\)
2 \(2 D / 5\)
3 \(D / 5\)
4 \(D / 3\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365755 Two identical thin uniform rods of length \(L\) each are joined to form \(T\) shape as shown in the figure. The distance of centre of mass from \(D\) is
supporting img

1 0
2 \(L / 4\)
3 \(3 L / 4\)
4 \(L\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365756 Assertion :
The centre of mass of uniform triangular lamina is centroid.
Reason :
Centroid is centre of symmetry of mass of the triangular lamina.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365757 A thin bar of length \(L\) has a mass per unit length \(\lambda\), that increases linearly with distance from one end. If its total mass is \(\mathrm{M}\) and its mass per unit length at the lighter end is \(\lambda_{0}\), then the distance of the centre of mass from the lighter end is :-

1 \(\frac{{2\;L}}{3} - \frac{{{\lambda _0}\;{L^2}}}{{6M}}\)
2 \(\frac{L}{3} + \frac{{{\lambda _0}\;{L^2}}}{{8M}}\)
3 \(\frac{L}{2} - \frac{{{\lambda _0}{L^2}}}{{4M}}\)
4 \(\frac{L}{3} + \frac{{{\lambda _0}\;{L^2}}}{{4M}}\)
JEE - 2014
For More Updates join with Us
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365754 Five uniform circular plates, each of diameter \(D\) and mass \(m\) are laid out in a pattern shown. Using the origin shown, find the \(y\) co-ordinate of the centre of mass of the five-plate system.
supporting img

1 \(4 D / 5\)
2 \(2 D / 5\)
3 \(D / 5\)
4 \(D / 3\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365755 Two identical thin uniform rods of length \(L\) each are joined to form \(T\) shape as shown in the figure. The distance of centre of mass from \(D\) is
supporting img

1 0
2 \(L / 4\)
3 \(3 L / 4\)
4 \(L\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365756 Assertion :
The centre of mass of uniform triangular lamina is centroid.
Reason :
Centroid is centre of symmetry of mass of the triangular lamina.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365757 A thin bar of length \(L\) has a mass per unit length \(\lambda\), that increases linearly with distance from one end. If its total mass is \(\mathrm{M}\) and its mass per unit length at the lighter end is \(\lambda_{0}\), then the distance of the centre of mass from the lighter end is :-

1 \(\frac{{2\;L}}{3} - \frac{{{\lambda _0}\;{L^2}}}{{6M}}\)
2 \(\frac{L}{3} + \frac{{{\lambda _0}\;{L^2}}}{{8M}}\)
3 \(\frac{L}{2} - \frac{{{\lambda _0}{L^2}}}{{4M}}\)
4 \(\frac{L}{3} + \frac{{{\lambda _0}\;{L^2}}}{{4M}}\)
JEE - 2014