Rigid Body Constraints
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366071 A wheel rolls along the ground with a speed of \(2\;\,m{s^{ - 1}}\). The magnitude of the velocity of the points at the extermities of the horizontal diameter of the wheel is equal to

1 \(2\sqrt 3 \;m{s^{ - 1}}\)
2 \(2\sqrt {10} \;\,m{s^{ - 1}}\)
3 \(2\;\,m{s^{ - 1}}\)
4 \(2\sqrt 2 \,\;m{s^{ - 1}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366072 A block is connected by an inextensible string. The pulley of radius \(R\) is unwinding at an acceleration \(\alpha\) and the block is going down with acceleration \(a\). The relation between \(a\) and \(\alpha\) is
supporting img

1 \(a=2 R \alpha\)
2 \(\alpha=a R\)
3 \(a=R \alpha\)
4 \(a=\dfrac{\alpha}{R}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366073 Two identical uniform discs of mass \(m\) and radius \(\mathrm{r}\) are arranged as shown in the figure. If \(\alpha\) is the angular acceleration of the lower disc and \(a_{c m}\) is acceleration of centre of mass of the lower disc, then relation among \(a_{c m}, \alpha\) and \(\mathrm{r}\) is:
supporting img

1 \(a_{c m}=\alpha r\)
2 \(a_{c m}=\dfrac{\alpha}{r}\)
3 \(a_{c m}=2 \alpha r\)
4 None of these
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366071 A wheel rolls along the ground with a speed of \(2\;\,m{s^{ - 1}}\). The magnitude of the velocity of the points at the extermities of the horizontal diameter of the wheel is equal to

1 \(2\sqrt 3 \;m{s^{ - 1}}\)
2 \(2\sqrt {10} \;\,m{s^{ - 1}}\)
3 \(2\;\,m{s^{ - 1}}\)
4 \(2\sqrt 2 \,\;m{s^{ - 1}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366072 A block is connected by an inextensible string. The pulley of radius \(R\) is unwinding at an acceleration \(\alpha\) and the block is going down with acceleration \(a\). The relation between \(a\) and \(\alpha\) is
supporting img

1 \(a=2 R \alpha\)
2 \(\alpha=a R\)
3 \(a=R \alpha\)
4 \(a=\dfrac{\alpha}{R}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366073 Two identical uniform discs of mass \(m\) and radius \(\mathrm{r}\) are arranged as shown in the figure. If \(\alpha\) is the angular acceleration of the lower disc and \(a_{c m}\) is acceleration of centre of mass of the lower disc, then relation among \(a_{c m}, \alpha\) and \(\mathrm{r}\) is:
supporting img

1 \(a_{c m}=\alpha r\)
2 \(a_{c m}=\dfrac{\alpha}{r}\)
3 \(a_{c m}=2 \alpha r\)
4 None of these
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366071 A wheel rolls along the ground with a speed of \(2\;\,m{s^{ - 1}}\). The magnitude of the velocity of the points at the extermities of the horizontal diameter of the wheel is equal to

1 \(2\sqrt 3 \;m{s^{ - 1}}\)
2 \(2\sqrt {10} \;\,m{s^{ - 1}}\)
3 \(2\;\,m{s^{ - 1}}\)
4 \(2\sqrt 2 \,\;m{s^{ - 1}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366072 A block is connected by an inextensible string. The pulley of radius \(R\) is unwinding at an acceleration \(\alpha\) and the block is going down with acceleration \(a\). The relation between \(a\) and \(\alpha\) is
supporting img

1 \(a=2 R \alpha\)
2 \(\alpha=a R\)
3 \(a=R \alpha\)
4 \(a=\dfrac{\alpha}{R}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366073 Two identical uniform discs of mass \(m\) and radius \(\mathrm{r}\) are arranged as shown in the figure. If \(\alpha\) is the angular acceleration of the lower disc and \(a_{c m}\) is acceleration of centre of mass of the lower disc, then relation among \(a_{c m}, \alpha\) and \(\mathrm{r}\) is:
supporting img

1 \(a_{c m}=\alpha r\)
2 \(a_{c m}=\dfrac{\alpha}{r}\)
3 \(a_{c m}=2 \alpha r\)
4 None of these
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