149671
The \(X\) and \(Y\) coordinates of the three particles of masses \(m, 2 m\) and \(3 m\) are respectively \((0,0)\) \((1,0)\) and \((-2,0)\). The X-coordinate of the centre of mass of the system is
1 \(\frac{1}{3}\)
2 \(\frac{2}{3}\)
3 \(-\frac{1}{3}\)
4 \(-\frac{2}{3}\)
5 \(\frac{1}{6}\)
Explanation:
D Centre of mass of the system, \(\overrightarrow{\mathrm{x}}_{\mathrm{com}}=\frac{\mathrm{m}_{1} \mathrm{x}_{1}+\mathrm{m}_{2} \mathrm{x}_{2}+\mathrm{m}_{3} \mathrm{x}_{3}}{\mathrm{~m}_{1}+\mathrm{m}_{2}+\mathrm{m}_{3}}\) \(\mathrm{x}_{\mathrm{com}}=\frac{[\mathrm{m} \times 0]+[2 \mathrm{~m} \times 1]+[3 \mathrm{~m} \times(-2)]}{[\mathrm{m}+2 \mathrm{~m}+3 \mathrm{~m}]}\) \(\mathrm{x}_{\mathrm{com}}=\frac{-4 \mathrm{~m}}{6 \mathrm{~m}}\) \(\mathrm{x}_{\text {com }}=\frac{-2}{3}\)
Kerala CEE 2021
Rotational Motion
149673
The sum of moments of all the particles in a system about its center of mass is always
1 Minimum
2 Zero
3 Maximum
4 Infinite
Explanation:
B Moment of mass \(=\) Distance \(\times\) Mass \(\mathrm{MX}_{\mathrm{cm}}=\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{m}_{1} \mathrm{X}_{\mathrm{c}}=\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{m}_{1} \mathrm{X}_{\mathrm{i}}\) \(\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{m}_{1}\left(\mathrm{X}_{\mathrm{c}}-\mathrm{X}_{\mathrm{i}}\right)=0\)
AP EAMCET-19.08.2021
Rotational Motion
149678
The centre of mass of a ring is
1 Outside the material of the \(\overline{\text { body at }}\) the centre of symmetry
2 Within the material of the body, at the centre of symmetry
3 Along a tangent of the ring
4 Perpendicular to edge of a ring
Explanation:
A The centre of mass of a ring is outside the material of the body, at the centre of symmetry.
AP EAMCET-24.09.2020
Rotational Motion
149679
The center of mass on combining two masses \(m\) in and \(M(M>m)\) will be
1 Towards \(m\)
2 Towards \(\mathrm{M}\)
3 At the center of line joining \(\mathrm{m}\) and \(\mathrm{M}\)
4 At centre of mass of \(m\)
Explanation:
B We know that, Center of mass depend of mass distribution. \(\mathrm{r}_{\mathrm{c}}=\left(\frac{\mathrm{mr}+\mathrm{mR}}{\mathrm{m}+\mathrm{M}}\right)\) Given, \(M>m\) Therefore, the centre of the mass of the system will be towards M
AP EAMCET-24.09.2020
Rotational Motion
149684
Centre of mass is a point
1 which is the geometric centre of a body.
2 which is the origin of reference frame.
3 where the whole mass of the body is supposed to be concentrated.
4 from which distances of all particles are same.
Explanation:
C Centre of mass of a body is a point at which the whole of the mass of the body supposed to be concentrated. Center of mass
149671
The \(X\) and \(Y\) coordinates of the three particles of masses \(m, 2 m\) and \(3 m\) are respectively \((0,0)\) \((1,0)\) and \((-2,0)\). The X-coordinate of the centre of mass of the system is
1 \(\frac{1}{3}\)
2 \(\frac{2}{3}\)
3 \(-\frac{1}{3}\)
4 \(-\frac{2}{3}\)
5 \(\frac{1}{6}\)
Explanation:
D Centre of mass of the system, \(\overrightarrow{\mathrm{x}}_{\mathrm{com}}=\frac{\mathrm{m}_{1} \mathrm{x}_{1}+\mathrm{m}_{2} \mathrm{x}_{2}+\mathrm{m}_{3} \mathrm{x}_{3}}{\mathrm{~m}_{1}+\mathrm{m}_{2}+\mathrm{m}_{3}}\) \(\mathrm{x}_{\mathrm{com}}=\frac{[\mathrm{m} \times 0]+[2 \mathrm{~m} \times 1]+[3 \mathrm{~m} \times(-2)]}{[\mathrm{m}+2 \mathrm{~m}+3 \mathrm{~m}]}\) \(\mathrm{x}_{\mathrm{com}}=\frac{-4 \mathrm{~m}}{6 \mathrm{~m}}\) \(\mathrm{x}_{\text {com }}=\frac{-2}{3}\)
Kerala CEE 2021
Rotational Motion
149673
The sum of moments of all the particles in a system about its center of mass is always
1 Minimum
2 Zero
3 Maximum
4 Infinite
Explanation:
B Moment of mass \(=\) Distance \(\times\) Mass \(\mathrm{MX}_{\mathrm{cm}}=\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{m}_{1} \mathrm{X}_{\mathrm{c}}=\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{m}_{1} \mathrm{X}_{\mathrm{i}}\) \(\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{m}_{1}\left(\mathrm{X}_{\mathrm{c}}-\mathrm{X}_{\mathrm{i}}\right)=0\)
AP EAMCET-19.08.2021
Rotational Motion
149678
The centre of mass of a ring is
1 Outside the material of the \(\overline{\text { body at }}\) the centre of symmetry
2 Within the material of the body, at the centre of symmetry
3 Along a tangent of the ring
4 Perpendicular to edge of a ring
Explanation:
A The centre of mass of a ring is outside the material of the body, at the centre of symmetry.
AP EAMCET-24.09.2020
Rotational Motion
149679
The center of mass on combining two masses \(m\) in and \(M(M>m)\) will be
1 Towards \(m\)
2 Towards \(\mathrm{M}\)
3 At the center of line joining \(\mathrm{m}\) and \(\mathrm{M}\)
4 At centre of mass of \(m\)
Explanation:
B We know that, Center of mass depend of mass distribution. \(\mathrm{r}_{\mathrm{c}}=\left(\frac{\mathrm{mr}+\mathrm{mR}}{\mathrm{m}+\mathrm{M}}\right)\) Given, \(M>m\) Therefore, the centre of the mass of the system will be towards M
AP EAMCET-24.09.2020
Rotational Motion
149684
Centre of mass is a point
1 which is the geometric centre of a body.
2 which is the origin of reference frame.
3 where the whole mass of the body is supposed to be concentrated.
4 from which distances of all particles are same.
Explanation:
C Centre of mass of a body is a point at which the whole of the mass of the body supposed to be concentrated. Center of mass
149671
The \(X\) and \(Y\) coordinates of the three particles of masses \(m, 2 m\) and \(3 m\) are respectively \((0,0)\) \((1,0)\) and \((-2,0)\). The X-coordinate of the centre of mass of the system is
1 \(\frac{1}{3}\)
2 \(\frac{2}{3}\)
3 \(-\frac{1}{3}\)
4 \(-\frac{2}{3}\)
5 \(\frac{1}{6}\)
Explanation:
D Centre of mass of the system, \(\overrightarrow{\mathrm{x}}_{\mathrm{com}}=\frac{\mathrm{m}_{1} \mathrm{x}_{1}+\mathrm{m}_{2} \mathrm{x}_{2}+\mathrm{m}_{3} \mathrm{x}_{3}}{\mathrm{~m}_{1}+\mathrm{m}_{2}+\mathrm{m}_{3}}\) \(\mathrm{x}_{\mathrm{com}}=\frac{[\mathrm{m} \times 0]+[2 \mathrm{~m} \times 1]+[3 \mathrm{~m} \times(-2)]}{[\mathrm{m}+2 \mathrm{~m}+3 \mathrm{~m}]}\) \(\mathrm{x}_{\mathrm{com}}=\frac{-4 \mathrm{~m}}{6 \mathrm{~m}}\) \(\mathrm{x}_{\text {com }}=\frac{-2}{3}\)
Kerala CEE 2021
Rotational Motion
149673
The sum of moments of all the particles in a system about its center of mass is always
1 Minimum
2 Zero
3 Maximum
4 Infinite
Explanation:
B Moment of mass \(=\) Distance \(\times\) Mass \(\mathrm{MX}_{\mathrm{cm}}=\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{m}_{1} \mathrm{X}_{\mathrm{c}}=\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{m}_{1} \mathrm{X}_{\mathrm{i}}\) \(\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{m}_{1}\left(\mathrm{X}_{\mathrm{c}}-\mathrm{X}_{\mathrm{i}}\right)=0\)
AP EAMCET-19.08.2021
Rotational Motion
149678
The centre of mass of a ring is
1 Outside the material of the \(\overline{\text { body at }}\) the centre of symmetry
2 Within the material of the body, at the centre of symmetry
3 Along a tangent of the ring
4 Perpendicular to edge of a ring
Explanation:
A The centre of mass of a ring is outside the material of the body, at the centre of symmetry.
AP EAMCET-24.09.2020
Rotational Motion
149679
The center of mass on combining two masses \(m\) in and \(M(M>m)\) will be
1 Towards \(m\)
2 Towards \(\mathrm{M}\)
3 At the center of line joining \(\mathrm{m}\) and \(\mathrm{M}\)
4 At centre of mass of \(m\)
Explanation:
B We know that, Center of mass depend of mass distribution. \(\mathrm{r}_{\mathrm{c}}=\left(\frac{\mathrm{mr}+\mathrm{mR}}{\mathrm{m}+\mathrm{M}}\right)\) Given, \(M>m\) Therefore, the centre of the mass of the system will be towards M
AP EAMCET-24.09.2020
Rotational Motion
149684
Centre of mass is a point
1 which is the geometric centre of a body.
2 which is the origin of reference frame.
3 where the whole mass of the body is supposed to be concentrated.
4 from which distances of all particles are same.
Explanation:
C Centre of mass of a body is a point at which the whole of the mass of the body supposed to be concentrated. Center of mass
NEET Test Series from KOTA - 10 Papers In MS WORD
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Rotational Motion
149671
The \(X\) and \(Y\) coordinates of the three particles of masses \(m, 2 m\) and \(3 m\) are respectively \((0,0)\) \((1,0)\) and \((-2,0)\). The X-coordinate of the centre of mass of the system is
1 \(\frac{1}{3}\)
2 \(\frac{2}{3}\)
3 \(-\frac{1}{3}\)
4 \(-\frac{2}{3}\)
5 \(\frac{1}{6}\)
Explanation:
D Centre of mass of the system, \(\overrightarrow{\mathrm{x}}_{\mathrm{com}}=\frac{\mathrm{m}_{1} \mathrm{x}_{1}+\mathrm{m}_{2} \mathrm{x}_{2}+\mathrm{m}_{3} \mathrm{x}_{3}}{\mathrm{~m}_{1}+\mathrm{m}_{2}+\mathrm{m}_{3}}\) \(\mathrm{x}_{\mathrm{com}}=\frac{[\mathrm{m} \times 0]+[2 \mathrm{~m} \times 1]+[3 \mathrm{~m} \times(-2)]}{[\mathrm{m}+2 \mathrm{~m}+3 \mathrm{~m}]}\) \(\mathrm{x}_{\mathrm{com}}=\frac{-4 \mathrm{~m}}{6 \mathrm{~m}}\) \(\mathrm{x}_{\text {com }}=\frac{-2}{3}\)
Kerala CEE 2021
Rotational Motion
149673
The sum of moments of all the particles in a system about its center of mass is always
1 Minimum
2 Zero
3 Maximum
4 Infinite
Explanation:
B Moment of mass \(=\) Distance \(\times\) Mass \(\mathrm{MX}_{\mathrm{cm}}=\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{m}_{1} \mathrm{X}_{\mathrm{c}}=\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{m}_{1} \mathrm{X}_{\mathrm{i}}\) \(\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{m}_{1}\left(\mathrm{X}_{\mathrm{c}}-\mathrm{X}_{\mathrm{i}}\right)=0\)
AP EAMCET-19.08.2021
Rotational Motion
149678
The centre of mass of a ring is
1 Outside the material of the \(\overline{\text { body at }}\) the centre of symmetry
2 Within the material of the body, at the centre of symmetry
3 Along a tangent of the ring
4 Perpendicular to edge of a ring
Explanation:
A The centre of mass of a ring is outside the material of the body, at the centre of symmetry.
AP EAMCET-24.09.2020
Rotational Motion
149679
The center of mass on combining two masses \(m\) in and \(M(M>m)\) will be
1 Towards \(m\)
2 Towards \(\mathrm{M}\)
3 At the center of line joining \(\mathrm{m}\) and \(\mathrm{M}\)
4 At centre of mass of \(m\)
Explanation:
B We know that, Center of mass depend of mass distribution. \(\mathrm{r}_{\mathrm{c}}=\left(\frac{\mathrm{mr}+\mathrm{mR}}{\mathrm{m}+\mathrm{M}}\right)\) Given, \(M>m\) Therefore, the centre of the mass of the system will be towards M
AP EAMCET-24.09.2020
Rotational Motion
149684
Centre of mass is a point
1 which is the geometric centre of a body.
2 which is the origin of reference frame.
3 where the whole mass of the body is supposed to be concentrated.
4 from which distances of all particles are same.
Explanation:
C Centre of mass of a body is a point at which the whole of the mass of the body supposed to be concentrated. Center of mass
149671
The \(X\) and \(Y\) coordinates of the three particles of masses \(m, 2 m\) and \(3 m\) are respectively \((0,0)\) \((1,0)\) and \((-2,0)\). The X-coordinate of the centre of mass of the system is
1 \(\frac{1}{3}\)
2 \(\frac{2}{3}\)
3 \(-\frac{1}{3}\)
4 \(-\frac{2}{3}\)
5 \(\frac{1}{6}\)
Explanation:
D Centre of mass of the system, \(\overrightarrow{\mathrm{x}}_{\mathrm{com}}=\frac{\mathrm{m}_{1} \mathrm{x}_{1}+\mathrm{m}_{2} \mathrm{x}_{2}+\mathrm{m}_{3} \mathrm{x}_{3}}{\mathrm{~m}_{1}+\mathrm{m}_{2}+\mathrm{m}_{3}}\) \(\mathrm{x}_{\mathrm{com}}=\frac{[\mathrm{m} \times 0]+[2 \mathrm{~m} \times 1]+[3 \mathrm{~m} \times(-2)]}{[\mathrm{m}+2 \mathrm{~m}+3 \mathrm{~m}]}\) \(\mathrm{x}_{\mathrm{com}}=\frac{-4 \mathrm{~m}}{6 \mathrm{~m}}\) \(\mathrm{x}_{\text {com }}=\frac{-2}{3}\)
Kerala CEE 2021
Rotational Motion
149673
The sum of moments of all the particles in a system about its center of mass is always
1 Minimum
2 Zero
3 Maximum
4 Infinite
Explanation:
B Moment of mass \(=\) Distance \(\times\) Mass \(\mathrm{MX}_{\mathrm{cm}}=\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{m}_{1} \mathrm{X}_{\mathrm{c}}=\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{m}_{1} \mathrm{X}_{\mathrm{i}}\) \(\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{m}_{1}\left(\mathrm{X}_{\mathrm{c}}-\mathrm{X}_{\mathrm{i}}\right)=0\)
AP EAMCET-19.08.2021
Rotational Motion
149678
The centre of mass of a ring is
1 Outside the material of the \(\overline{\text { body at }}\) the centre of symmetry
2 Within the material of the body, at the centre of symmetry
3 Along a tangent of the ring
4 Perpendicular to edge of a ring
Explanation:
A The centre of mass of a ring is outside the material of the body, at the centre of symmetry.
AP EAMCET-24.09.2020
Rotational Motion
149679
The center of mass on combining two masses \(m\) in and \(M(M>m)\) will be
1 Towards \(m\)
2 Towards \(\mathrm{M}\)
3 At the center of line joining \(\mathrm{m}\) and \(\mathrm{M}\)
4 At centre of mass of \(m\)
Explanation:
B We know that, Center of mass depend of mass distribution. \(\mathrm{r}_{\mathrm{c}}=\left(\frac{\mathrm{mr}+\mathrm{mR}}{\mathrm{m}+\mathrm{M}}\right)\) Given, \(M>m\) Therefore, the centre of the mass of the system will be towards M
AP EAMCET-24.09.2020
Rotational Motion
149684
Centre of mass is a point
1 which is the geometric centre of a body.
2 which is the origin of reference frame.
3 where the whole mass of the body is supposed to be concentrated.
4 from which distances of all particles are same.
Explanation:
C Centre of mass of a body is a point at which the whole of the mass of the body supposed to be concentrated. Center of mass
