00. Centre of Mass
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Rotational Motion

149660 Two objects \(P\) and \(Q\) initially at rest move towards each other under mutual force of attraction. At the instant when the velocity of \(P\) is \(v\) and that of \(Q\) is \(2 v\), the velocity of centre of mass of the system is

1 \(\mathrm{v}\)
2 \(3 \mathrm{v}\)
3 \(2 \mathrm{v}\)
4 \(1.5 \mathrm{v}\)
5 zero
Karnataka CET-2019
Rotational Motion

149661 A circular disc of radius \(R\) is removed from one end of a bigger circular disc of radius \(2 R\). The centre of mass of the new disc is at a distance \(\alpha R\) from the centre of the bigger disc. The value of \(\alpha\) is

1 \(\frac{1}{2}\)
2 \(\frac{1}{3}\)
3 \(\frac{1}{4}\)
4 \(\frac{1}{6}\)
AP EAMCET (20.04.2019) Shift-1
Rotational Motion

149662 Two bodies of mass \(1 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) have position vectors \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(-3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector:

1 \(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}\)
2 \(-3 \hat{i}-2 \hat{j}+\hat{k}\)
3 \(-2 \hat{j}+2 \hat{k}\)
4 \(-2 \hat{i}-\hat{j}+2 \hat{k}\)
JEE Main-29.07.2022
Rotational Motion

149663 A circular portion of radius \(R_{2}\) has been removed from one edge of a circular disc of radius \(\mathbf{R}_{1}\). The correct expression for the centre of mass for the remaining portion of the disc is-

1 \(-\frac{R_{2}^{2}}{R_{1}+R_{2}}\)
2 \(-\frac{R_{2}^{2}}{R_{1}+R_{2}}\)
3 \(\frac{\mathrm{R}_{2}^{2}}{\mathrm{R}_{1}+\mathrm{R}_{2}}\)
4 \(-\frac{R_{1}^{2}}{R_{1}+R_{2}}\)
AP EAMCET-08.07.2022
Rotational Motion

149664 A solid circular disc of mass \(100 \mathrm{~kg}\) rolls along a horizontal floor so that center of mass of the disc has a speed of \(0.2 \mathrm{~m} \mathrm{~s}^{-1}\). The absolute value of work done on the disc to stop it is

1 \(2 \mathrm{~J}\)
2 \(3 \mathrm{~J}\)
3 \(2.5 \mathrm{~J}\)
4 \(4 \mathrm{~J}\)
AP EAMCET-12.07.2022
NEET DIGITAL LIBRARY
Rotational Motion

149660 Two objects \(P\) and \(Q\) initially at rest move towards each other under mutual force of attraction. At the instant when the velocity of \(P\) is \(v\) and that of \(Q\) is \(2 v\), the velocity of centre of mass of the system is

1 \(\mathrm{v}\)
2 \(3 \mathrm{v}\)
3 \(2 \mathrm{v}\)
4 \(1.5 \mathrm{v}\)
5 zero
Karnataka CET-2019
Rotational Motion

149661 A circular disc of radius \(R\) is removed from one end of a bigger circular disc of radius \(2 R\). The centre of mass of the new disc is at a distance \(\alpha R\) from the centre of the bigger disc. The value of \(\alpha\) is

1 \(\frac{1}{2}\)
2 \(\frac{1}{3}\)
3 \(\frac{1}{4}\)
4 \(\frac{1}{6}\)
AP EAMCET (20.04.2019) Shift-1
Rotational Motion

149662 Two bodies of mass \(1 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) have position vectors \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(-3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector:

1 \(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}\)
2 \(-3 \hat{i}-2 \hat{j}+\hat{k}\)
3 \(-2 \hat{j}+2 \hat{k}\)
4 \(-2 \hat{i}-\hat{j}+2 \hat{k}\)
JEE Main-29.07.2022
Rotational Motion

149663 A circular portion of radius \(R_{2}\) has been removed from one edge of a circular disc of radius \(\mathbf{R}_{1}\). The correct expression for the centre of mass for the remaining portion of the disc is-

1 \(-\frac{R_{2}^{2}}{R_{1}+R_{2}}\)
2 \(-\frac{R_{2}^{2}}{R_{1}+R_{2}}\)
3 \(\frac{\mathrm{R}_{2}^{2}}{\mathrm{R}_{1}+\mathrm{R}_{2}}\)
4 \(-\frac{R_{1}^{2}}{R_{1}+R_{2}}\)
AP EAMCET-08.07.2022
Rotational Motion

149664 A solid circular disc of mass \(100 \mathrm{~kg}\) rolls along a horizontal floor so that center of mass of the disc has a speed of \(0.2 \mathrm{~m} \mathrm{~s}^{-1}\). The absolute value of work done on the disc to stop it is

1 \(2 \mathrm{~J}\)
2 \(3 \mathrm{~J}\)
3 \(2.5 \mathrm{~J}\)
4 \(4 \mathrm{~J}\)
AP EAMCET-12.07.2022
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Rotational Motion

149660 Two objects \(P\) and \(Q\) initially at rest move towards each other under mutual force of attraction. At the instant when the velocity of \(P\) is \(v\) and that of \(Q\) is \(2 v\), the velocity of centre of mass of the system is

1 \(\mathrm{v}\)
2 \(3 \mathrm{v}\)
3 \(2 \mathrm{v}\)
4 \(1.5 \mathrm{v}\)
5 zero
Karnataka CET-2019
Rotational Motion

149661 A circular disc of radius \(R\) is removed from one end of a bigger circular disc of radius \(2 R\). The centre of mass of the new disc is at a distance \(\alpha R\) from the centre of the bigger disc. The value of \(\alpha\) is

1 \(\frac{1}{2}\)
2 \(\frac{1}{3}\)
3 \(\frac{1}{4}\)
4 \(\frac{1}{6}\)
AP EAMCET (20.04.2019) Shift-1
Rotational Motion

149662 Two bodies of mass \(1 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) have position vectors \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(-3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector:

1 \(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}\)
2 \(-3 \hat{i}-2 \hat{j}+\hat{k}\)
3 \(-2 \hat{j}+2 \hat{k}\)
4 \(-2 \hat{i}-\hat{j}+2 \hat{k}\)
JEE Main-29.07.2022
Rotational Motion

149663 A circular portion of radius \(R_{2}\) has been removed from one edge of a circular disc of radius \(\mathbf{R}_{1}\). The correct expression for the centre of mass for the remaining portion of the disc is-

1 \(-\frac{R_{2}^{2}}{R_{1}+R_{2}}\)
2 \(-\frac{R_{2}^{2}}{R_{1}+R_{2}}\)
3 \(\frac{\mathrm{R}_{2}^{2}}{\mathrm{R}_{1}+\mathrm{R}_{2}}\)
4 \(-\frac{R_{1}^{2}}{R_{1}+R_{2}}\)
AP EAMCET-08.07.2022
Rotational Motion

149664 A solid circular disc of mass \(100 \mathrm{~kg}\) rolls along a horizontal floor so that center of mass of the disc has a speed of \(0.2 \mathrm{~m} \mathrm{~s}^{-1}\). The absolute value of work done on the disc to stop it is

1 \(2 \mathrm{~J}\)
2 \(3 \mathrm{~J}\)
3 \(2.5 \mathrm{~J}\)
4 \(4 \mathrm{~J}\)
AP EAMCET-12.07.2022
For More Updates join with Us
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Rotational Motion

149660 Two objects \(P\) and \(Q\) initially at rest move towards each other under mutual force of attraction. At the instant when the velocity of \(P\) is \(v\) and that of \(Q\) is \(2 v\), the velocity of centre of mass of the system is

1 \(\mathrm{v}\)
2 \(3 \mathrm{v}\)
3 \(2 \mathrm{v}\)
4 \(1.5 \mathrm{v}\)
5 zero
Karnataka CET-2019
Rotational Motion

149661 A circular disc of radius \(R\) is removed from one end of a bigger circular disc of radius \(2 R\). The centre of mass of the new disc is at a distance \(\alpha R\) from the centre of the bigger disc. The value of \(\alpha\) is

1 \(\frac{1}{2}\)
2 \(\frac{1}{3}\)
3 \(\frac{1}{4}\)
4 \(\frac{1}{6}\)
AP EAMCET (20.04.2019) Shift-1
Rotational Motion

149662 Two bodies of mass \(1 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) have position vectors \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(-3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector:

1 \(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}\)
2 \(-3 \hat{i}-2 \hat{j}+\hat{k}\)
3 \(-2 \hat{j}+2 \hat{k}\)
4 \(-2 \hat{i}-\hat{j}+2 \hat{k}\)
JEE Main-29.07.2022
Rotational Motion

149663 A circular portion of radius \(R_{2}\) has been removed from one edge of a circular disc of radius \(\mathbf{R}_{1}\). The correct expression for the centre of mass for the remaining portion of the disc is-

1 \(-\frac{R_{2}^{2}}{R_{1}+R_{2}}\)
2 \(-\frac{R_{2}^{2}}{R_{1}+R_{2}}\)
3 \(\frac{\mathrm{R}_{2}^{2}}{\mathrm{R}_{1}+\mathrm{R}_{2}}\)
4 \(-\frac{R_{1}^{2}}{R_{1}+R_{2}}\)
AP EAMCET-08.07.2022
Rotational Motion

149664 A solid circular disc of mass \(100 \mathrm{~kg}\) rolls along a horizontal floor so that center of mass of the disc has a speed of \(0.2 \mathrm{~m} \mathrm{~s}^{-1}\). The absolute value of work done on the disc to stop it is

1 \(2 \mathrm{~J}\)
2 \(3 \mathrm{~J}\)
3 \(2.5 \mathrm{~J}\)
4 \(4 \mathrm{~J}\)
AP EAMCET-12.07.2022
NEET DIGITAL LIBRARY
Rotational Motion

149660 Two objects \(P\) and \(Q\) initially at rest move towards each other under mutual force of attraction. At the instant when the velocity of \(P\) is \(v\) and that of \(Q\) is \(2 v\), the velocity of centre of mass of the system is

1 \(\mathrm{v}\)
2 \(3 \mathrm{v}\)
3 \(2 \mathrm{v}\)
4 \(1.5 \mathrm{v}\)
5 zero
Karnataka CET-2019
Rotational Motion

149661 A circular disc of radius \(R\) is removed from one end of a bigger circular disc of radius \(2 R\). The centre of mass of the new disc is at a distance \(\alpha R\) from the centre of the bigger disc. The value of \(\alpha\) is

1 \(\frac{1}{2}\)
2 \(\frac{1}{3}\)
3 \(\frac{1}{4}\)
4 \(\frac{1}{6}\)
AP EAMCET (20.04.2019) Shift-1
Rotational Motion

149662 Two bodies of mass \(1 \mathrm{~kg}\) and \(3 \mathrm{~kg}\) have position vectors \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(-3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector:

1 \(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}\)
2 \(-3 \hat{i}-2 \hat{j}+\hat{k}\)
3 \(-2 \hat{j}+2 \hat{k}\)
4 \(-2 \hat{i}-\hat{j}+2 \hat{k}\)
JEE Main-29.07.2022
Rotational Motion

149663 A circular portion of radius \(R_{2}\) has been removed from one edge of a circular disc of radius \(\mathbf{R}_{1}\). The correct expression for the centre of mass for the remaining portion of the disc is-

1 \(-\frac{R_{2}^{2}}{R_{1}+R_{2}}\)
2 \(-\frac{R_{2}^{2}}{R_{1}+R_{2}}\)
3 \(\frac{\mathrm{R}_{2}^{2}}{\mathrm{R}_{1}+\mathrm{R}_{2}}\)
4 \(-\frac{R_{1}^{2}}{R_{1}+R_{2}}\)
AP EAMCET-08.07.2022
Rotational Motion

149664 A solid circular disc of mass \(100 \mathrm{~kg}\) rolls along a horizontal floor so that center of mass of the disc has a speed of \(0.2 \mathrm{~m} \mathrm{~s}^{-1}\). The absolute value of work done on the disc to stop it is

1 \(2 \mathrm{~J}\)
2 \(3 \mathrm{~J}\)
3 \(2.5 \mathrm{~J}\)
4 \(4 \mathrm{~J}\)
AP EAMCET-12.07.2022