00. Centre of Mass
Rotational Motion

149697 In the earth-moon system, if \(T_{1}\) and \(T_{2}\) are period of revolution of earth and moon respectively about the centre of mass of the system, then

1 \(\mathrm{T}_{1}>\mathrm{T}_{2}\)
2 \(T_{1}=T_{2}\)
3 \(\mathrm{T}_{1} \lt \mathrm{T}_{2}\)
4 Insufficient data
Rotational Motion

149705 Three circular discs of same material and same thickness of radii \(r, 2 r\) and \(3 r\) are placed on a horizontal plane such that their centres lie along a straight line. The radius of the middle disc is \(2 r\) and it touches the other two discs. The distance of the centre of mass of the system from the centre of the smaller disc is

1 \(2 \mathrm{r}\)
2 \(4 \mathrm{r}\)
3 \(6 \mathrm{r}\)
4 \(8 \mathrm{r}\)
Rotational Motion

149706 Two blocks of masses \(10 \mathrm{~kg}\) and \(2 \mathrm{Kg}\) are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of \(12 \mathrm{~ms}^{-1}\) to the heavier block in the direction of the lighter block. The velocity of centre of mass is:

1 \(30 \mathrm{~ms}^{-1}\)
2 \(10 \mathrm{~ms}^{-1}\)
3 \(20 \mathrm{~ms}^{-1}\)
4 \(5 \mathrm{~ms}-1\)
Rotational Motion

149707 Two particles \(A\) and \(B\) (both initially at rest) start moving towards each other under a mutual force of attraction. At the instant, when the speed of A is \(v\) and the speed of B is \(2 v\), the speed of the centre of mass is

1 zero
2 \(v\)
3 \(\frac{3 v}{2}\)
4 \(-\frac{3 v}{2}\)
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Rotational Motion

149697 In the earth-moon system, if \(T_{1}\) and \(T_{2}\) are period of revolution of earth and moon respectively about the centre of mass of the system, then

1 \(\mathrm{T}_{1}>\mathrm{T}_{2}\)
2 \(T_{1}=T_{2}\)
3 \(\mathrm{T}_{1} \lt \mathrm{T}_{2}\)
4 Insufficient data
Rotational Motion

149705 Three circular discs of same material and same thickness of radii \(r, 2 r\) and \(3 r\) are placed on a horizontal plane such that their centres lie along a straight line. The radius of the middle disc is \(2 r\) and it touches the other two discs. The distance of the centre of mass of the system from the centre of the smaller disc is

1 \(2 \mathrm{r}\)
2 \(4 \mathrm{r}\)
3 \(6 \mathrm{r}\)
4 \(8 \mathrm{r}\)
Rotational Motion

149706 Two blocks of masses \(10 \mathrm{~kg}\) and \(2 \mathrm{Kg}\) are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of \(12 \mathrm{~ms}^{-1}\) to the heavier block in the direction of the lighter block. The velocity of centre of mass is:

1 \(30 \mathrm{~ms}^{-1}\)
2 \(10 \mathrm{~ms}^{-1}\)
3 \(20 \mathrm{~ms}^{-1}\)
4 \(5 \mathrm{~ms}-1\)
Rotational Motion

149707 Two particles \(A\) and \(B\) (both initially at rest) start moving towards each other under a mutual force of attraction. At the instant, when the speed of A is \(v\) and the speed of B is \(2 v\), the speed of the centre of mass is

1 zero
2 \(v\)
3 \(\frac{3 v}{2}\)
4 \(-\frac{3 v}{2}\)
Rotational Motion

149697 In the earth-moon system, if \(T_{1}\) and \(T_{2}\) are period of revolution of earth and moon respectively about the centre of mass of the system, then

1 \(\mathrm{T}_{1}>\mathrm{T}_{2}\)
2 \(T_{1}=T_{2}\)
3 \(\mathrm{T}_{1} \lt \mathrm{T}_{2}\)
4 Insufficient data
Rotational Motion

149705 Three circular discs of same material and same thickness of radii \(r, 2 r\) and \(3 r\) are placed on a horizontal plane such that their centres lie along a straight line. The radius of the middle disc is \(2 r\) and it touches the other two discs. The distance of the centre of mass of the system from the centre of the smaller disc is

1 \(2 \mathrm{r}\)
2 \(4 \mathrm{r}\)
3 \(6 \mathrm{r}\)
4 \(8 \mathrm{r}\)
Rotational Motion

149706 Two blocks of masses \(10 \mathrm{~kg}\) and \(2 \mathrm{Kg}\) are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of \(12 \mathrm{~ms}^{-1}\) to the heavier block in the direction of the lighter block. The velocity of centre of mass is:

1 \(30 \mathrm{~ms}^{-1}\)
2 \(10 \mathrm{~ms}^{-1}\)
3 \(20 \mathrm{~ms}^{-1}\)
4 \(5 \mathrm{~ms}-1\)
Rotational Motion

149707 Two particles \(A\) and \(B\) (both initially at rest) start moving towards each other under a mutual force of attraction. At the instant, when the speed of A is \(v\) and the speed of B is \(2 v\), the speed of the centre of mass is

1 zero
2 \(v\)
3 \(\frac{3 v}{2}\)
4 \(-\frac{3 v}{2}\)
Rotational Motion

149697 In the earth-moon system, if \(T_{1}\) and \(T_{2}\) are period of revolution of earth and moon respectively about the centre of mass of the system, then

1 \(\mathrm{T}_{1}>\mathrm{T}_{2}\)
2 \(T_{1}=T_{2}\)
3 \(\mathrm{T}_{1} \lt \mathrm{T}_{2}\)
4 Insufficient data
Rotational Motion

149705 Three circular discs of same material and same thickness of radii \(r, 2 r\) and \(3 r\) are placed on a horizontal plane such that their centres lie along a straight line. The radius of the middle disc is \(2 r\) and it touches the other two discs. The distance of the centre of mass of the system from the centre of the smaller disc is

1 \(2 \mathrm{r}\)
2 \(4 \mathrm{r}\)
3 \(6 \mathrm{r}\)
4 \(8 \mathrm{r}\)
Rotational Motion

149706 Two blocks of masses \(10 \mathrm{~kg}\) and \(2 \mathrm{Kg}\) are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of \(12 \mathrm{~ms}^{-1}\) to the heavier block in the direction of the lighter block. The velocity of centre of mass is:

1 \(30 \mathrm{~ms}^{-1}\)
2 \(10 \mathrm{~ms}^{-1}\)
3 \(20 \mathrm{~ms}^{-1}\)
4 \(5 \mathrm{~ms}-1\)
Rotational Motion

149707 Two particles \(A\) and \(B\) (both initially at rest) start moving towards each other under a mutual force of attraction. At the instant, when the speed of A is \(v\) and the speed of B is \(2 v\), the speed of the centre of mass is

1 zero
2 \(v\)
3 \(\frac{3 v}{2}\)
4 \(-\frac{3 v}{2}\)