Centre of Mass
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365745 Assertion :
The centre of mass of two particle system lies on the line joining the two particles, being closer to the heavier particle.
Reason :
This is because product of mass of one particle and its distance from centre of mass is numerically equal to product of mass of other particle and its distance from centre of mass.

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

365746 From a uniform disc of radius \(R\), an equilateral triangle of side \(\sqrt{3} R\) is cut as shown in the figure. The new position of centre of mass is:
supporting img

1 \((0, \mathrm{R})\)
2 \((0,0)\)
3 \(\left(0, \dfrac{\sqrt{3} R}{2}\right)\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365747 From the circular disc of radius \(4R\) two small disc of radius \(R\) are cut off. The centre of mass of the new structure will be:
supporting img

1 \(i \dfrac{R}{5}+j \dfrac{R}{5}\)
2 \(-i \dfrac{R}{5}+j \dfrac{R}{5}\)
3 \(\dfrac{-3 R}{5}(\hat{i}+\hat{j})\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365748 Figure shows a square plate of uniform thickness and side length \(\sqrt 2 \;m\). One fourth of the plate is removed as indicated. The distance of centre of mass of the remaining portion from the centre of the original square plate is
supporting img

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

365745 Assertion :
The centre of mass of two particle system lies on the line joining the two particles, being closer to the heavier particle.
Reason :
This is because product of mass of one particle and its distance from centre of mass is numerically equal to product of mass of other particle and its distance from centre of mass.

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

365746 From a uniform disc of radius \(R\), an equilateral triangle of side \(\sqrt{3} R\) is cut as shown in the figure. The new position of centre of mass is:
supporting img

1 \((0, \mathrm{R})\)
2 \((0,0)\)
3 \(\left(0, \dfrac{\sqrt{3} R}{2}\right)\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365747 From the circular disc of radius \(4R\) two small disc of radius \(R\) are cut off. The centre of mass of the new structure will be:
supporting img

1 \(i \dfrac{R}{5}+j \dfrac{R}{5}\)
2 \(-i \dfrac{R}{5}+j \dfrac{R}{5}\)
3 \(\dfrac{-3 R}{5}(\hat{i}+\hat{j})\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365748 Figure shows a square plate of uniform thickness and side length \(\sqrt 2 \;m\). One fourth of the plate is removed as indicated. The distance of centre of mass of the remaining portion from the centre of the original square plate is
supporting img

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

365745 Assertion :
The centre of mass of two particle system lies on the line joining the two particles, being closer to the heavier particle.
Reason :
This is because product of mass of one particle and its distance from centre of mass is numerically equal to product of mass of other particle and its distance from centre of mass.

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

365746 From a uniform disc of radius \(R\), an equilateral triangle of side \(\sqrt{3} R\) is cut as shown in the figure. The new position of centre of mass is:
supporting img

1 \((0, \mathrm{R})\)
2 \((0,0)\)
3 \(\left(0, \dfrac{\sqrt{3} R}{2}\right)\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365747 From the circular disc of radius \(4R\) two small disc of radius \(R\) are cut off. The centre of mass of the new structure will be:
supporting img

1 \(i \dfrac{R}{5}+j \dfrac{R}{5}\)
2 \(-i \dfrac{R}{5}+j \dfrac{R}{5}\)
3 \(\dfrac{-3 R}{5}(\hat{i}+\hat{j})\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365748 Figure shows a square plate of uniform thickness and side length \(\sqrt 2 \;m\). One fourth of the plate is removed as indicated. The distance of centre of mass of the remaining portion from the centre of the original square plate is
supporting img

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

365745 Assertion :
The centre of mass of two particle system lies on the line joining the two particles, being closer to the heavier particle.
Reason :
This is because product of mass of one particle and its distance from centre of mass is numerically equal to product of mass of other particle and its distance from centre of mass.

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

365746 From a uniform disc of radius \(R\), an equilateral triangle of side \(\sqrt{3} R\) is cut as shown in the figure. The new position of centre of mass is:
supporting img

1 \((0, \mathrm{R})\)
2 \((0,0)\)
3 \(\left(0, \dfrac{\sqrt{3} R}{2}\right)\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365747 From the circular disc of radius \(4R\) two small disc of radius \(R\) are cut off. The centre of mass of the new structure will be:
supporting img

1 \(i \dfrac{R}{5}+j \dfrac{R}{5}\)
2 \(-i \dfrac{R}{5}+j \dfrac{R}{5}\)
3 \(\dfrac{-3 R}{5}(\hat{i}+\hat{j})\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365748 Figure shows a square plate of uniform thickness and side length \(\sqrt 2 \;m\). One fourth of the plate is removed as indicated. The distance of centre of mass of the remaining portion from the centre of the original square plate is
supporting img

1 \(1{\rm{/}}3{\mkern 1mu} \,m\)
2 \(1{\rm{/}}2{\mkern 1mu} \,m\)
3 \(1{\rm{/}}6{\mkern 1mu} \,m\)
4 \(1{\rm{/}}8{\mkern 1mu} \,m\)