361854
A particle revolving in a circular path completes first one third of circumference in \(2\,{\rm{sec}}\), while next one third in \(1\,{\rm{sec}}\). The average angular velocity of particle will be (in \(rad{\rm{/}}\sec \) )
1 \(\dfrac{4 \pi}{3}\)
2 \(\dfrac{\pi}{3}\)
3 \(\dfrac{4 \pi}{5}\)
4 \(\dfrac{5 \pi}{3}\)
Explanation:
We have \(\vec{\omega}_{a v}=\dfrac{\text { Total angular displacement }}{\text { Total time }}\) For first one third part of circle, angular displacement, \({\theta _1} = \frac{{{S_1}}}{r} = \frac{{2\pi r/3}}{r} = \frac{{2\pi }}{3}rad\) For second one third part of circle, \({\theta _2} = \frac{{2\pi r/3}}{r} = \frac{{2\pi }}{3}rad\) Total angular displacement, \(\theta = {\theta _1} + {\theta _2} = 4\pi {\rm{/}}3\,rad\) Total time \( = 2 + 1 = 3\,{\rm{sec}}\) \(\therefore {\vec \omega _{av}} = \frac{{4\pi {\rm{/}}3}}{3}rad{\rm{/}}s = \frac{{4\pi }}{3}rad{\rm{/}}s\)
PHXI04:MOTION IN A PLANE
361855
A wheel is of diameter \({1 m}\). If it makes 30 revolutions/ sec , then the linear speed of a point on its circumference will be
361856
The ratio of angular speed of a second-hand to the hour-hand of a watch is
1 \(60:1\)
2 \(72:1\)
3 \(720:1\)
4 \(3600:1\)
Explanation:
The second-hand completes one rotation in 1 min and the hour-hand completes in 12 \(h\). \(\therefore \) The angular speed of the second-hand is \({\omega _s} = \frac{{2\pi \,rad}}{{1\,\min }} = \frac{{2\pi \,rad}}{{60\,s}}\) and that of the hour-hand is \({\omega _h} = \frac{{2\pi \,rad}}{{12\,h}} = \frac{{2\pi \,rad}}{{12 \times 60 \times 60\,s}}\) \(\frac{{{\omega _s}}}{{{\omega _h}}} = \frac{{\frac{{2\pi \,rad}}{{60\,s}}}}{{\frac{{2\pi \,rad}}{{12 \times 60 \times 60\,s}}}} = 720\)
361854
A particle revolving in a circular path completes first one third of circumference in \(2\,{\rm{sec}}\), while next one third in \(1\,{\rm{sec}}\). The average angular velocity of particle will be (in \(rad{\rm{/}}\sec \) )
1 \(\dfrac{4 \pi}{3}\)
2 \(\dfrac{\pi}{3}\)
3 \(\dfrac{4 \pi}{5}\)
4 \(\dfrac{5 \pi}{3}\)
Explanation:
We have \(\vec{\omega}_{a v}=\dfrac{\text { Total angular displacement }}{\text { Total time }}\) For first one third part of circle, angular displacement, \({\theta _1} = \frac{{{S_1}}}{r} = \frac{{2\pi r/3}}{r} = \frac{{2\pi }}{3}rad\) For second one third part of circle, \({\theta _2} = \frac{{2\pi r/3}}{r} = \frac{{2\pi }}{3}rad\) Total angular displacement, \(\theta = {\theta _1} + {\theta _2} = 4\pi {\rm{/}}3\,rad\) Total time \( = 2 + 1 = 3\,{\rm{sec}}\) \(\therefore {\vec \omega _{av}} = \frac{{4\pi {\rm{/}}3}}{3}rad{\rm{/}}s = \frac{{4\pi }}{3}rad{\rm{/}}s\)
PHXI04:MOTION IN A PLANE
361855
A wheel is of diameter \({1 m}\). If it makes 30 revolutions/ sec , then the linear speed of a point on its circumference will be
361856
The ratio of angular speed of a second-hand to the hour-hand of a watch is
1 \(60:1\)
2 \(72:1\)
3 \(720:1\)
4 \(3600:1\)
Explanation:
The second-hand completes one rotation in 1 min and the hour-hand completes in 12 \(h\). \(\therefore \) The angular speed of the second-hand is \({\omega _s} = \frac{{2\pi \,rad}}{{1\,\min }} = \frac{{2\pi \,rad}}{{60\,s}}\) and that of the hour-hand is \({\omega _h} = \frac{{2\pi \,rad}}{{12\,h}} = \frac{{2\pi \,rad}}{{12 \times 60 \times 60\,s}}\) \(\frac{{{\omega _s}}}{{{\omega _h}}} = \frac{{\frac{{2\pi \,rad}}{{60\,s}}}}{{\frac{{2\pi \,rad}}{{12 \times 60 \times 60\,s}}}} = 720\)
361854
A particle revolving in a circular path completes first one third of circumference in \(2\,{\rm{sec}}\), while next one third in \(1\,{\rm{sec}}\). The average angular velocity of particle will be (in \(rad{\rm{/}}\sec \) )
1 \(\dfrac{4 \pi}{3}\)
2 \(\dfrac{\pi}{3}\)
3 \(\dfrac{4 \pi}{5}\)
4 \(\dfrac{5 \pi}{3}\)
Explanation:
We have \(\vec{\omega}_{a v}=\dfrac{\text { Total angular displacement }}{\text { Total time }}\) For first one third part of circle, angular displacement, \({\theta _1} = \frac{{{S_1}}}{r} = \frac{{2\pi r/3}}{r} = \frac{{2\pi }}{3}rad\) For second one third part of circle, \({\theta _2} = \frac{{2\pi r/3}}{r} = \frac{{2\pi }}{3}rad\) Total angular displacement, \(\theta = {\theta _1} + {\theta _2} = 4\pi {\rm{/}}3\,rad\) Total time \( = 2 + 1 = 3\,{\rm{sec}}\) \(\therefore {\vec \omega _{av}} = \frac{{4\pi {\rm{/}}3}}{3}rad{\rm{/}}s = \frac{{4\pi }}{3}rad{\rm{/}}s\)
PHXI04:MOTION IN A PLANE
361855
A wheel is of diameter \({1 m}\). If it makes 30 revolutions/ sec , then the linear speed of a point on its circumference will be
361856
The ratio of angular speed of a second-hand to the hour-hand of a watch is
1 \(60:1\)
2 \(72:1\)
3 \(720:1\)
4 \(3600:1\)
Explanation:
The second-hand completes one rotation in 1 min and the hour-hand completes in 12 \(h\). \(\therefore \) The angular speed of the second-hand is \({\omega _s} = \frac{{2\pi \,rad}}{{1\,\min }} = \frac{{2\pi \,rad}}{{60\,s}}\) and that of the hour-hand is \({\omega _h} = \frac{{2\pi \,rad}}{{12\,h}} = \frac{{2\pi \,rad}}{{12 \times 60 \times 60\,s}}\) \(\frac{{{\omega _s}}}{{{\omega _h}}} = \frac{{\frac{{2\pi \,rad}}{{60\,s}}}}{{\frac{{2\pi \,rad}}{{12 \times 60 \times 60\,s}}}} = 720\)
361854
A particle revolving in a circular path completes first one third of circumference in \(2\,{\rm{sec}}\), while next one third in \(1\,{\rm{sec}}\). The average angular velocity of particle will be (in \(rad{\rm{/}}\sec \) )
1 \(\dfrac{4 \pi}{3}\)
2 \(\dfrac{\pi}{3}\)
3 \(\dfrac{4 \pi}{5}\)
4 \(\dfrac{5 \pi}{3}\)
Explanation:
We have \(\vec{\omega}_{a v}=\dfrac{\text { Total angular displacement }}{\text { Total time }}\) For first one third part of circle, angular displacement, \({\theta _1} = \frac{{{S_1}}}{r} = \frac{{2\pi r/3}}{r} = \frac{{2\pi }}{3}rad\) For second one third part of circle, \({\theta _2} = \frac{{2\pi r/3}}{r} = \frac{{2\pi }}{3}rad\) Total angular displacement, \(\theta = {\theta _1} + {\theta _2} = 4\pi {\rm{/}}3\,rad\) Total time \( = 2 + 1 = 3\,{\rm{sec}}\) \(\therefore {\vec \omega _{av}} = \frac{{4\pi {\rm{/}}3}}{3}rad{\rm{/}}s = \frac{{4\pi }}{3}rad{\rm{/}}s\)
PHXI04:MOTION IN A PLANE
361855
A wheel is of diameter \({1 m}\). If it makes 30 revolutions/ sec , then the linear speed of a point on its circumference will be
361856
The ratio of angular speed of a second-hand to the hour-hand of a watch is
1 \(60:1\)
2 \(72:1\)
3 \(720:1\)
4 \(3600:1\)
Explanation:
The second-hand completes one rotation in 1 min and the hour-hand completes in 12 \(h\). \(\therefore \) The angular speed of the second-hand is \({\omega _s} = \frac{{2\pi \,rad}}{{1\,\min }} = \frac{{2\pi \,rad}}{{60\,s}}\) and that of the hour-hand is \({\omega _h} = \frac{{2\pi \,rad}}{{12\,h}} = \frac{{2\pi \,rad}}{{12 \times 60 \times 60\,s}}\) \(\frac{{{\omega _s}}}{{{\omega _h}}} = \frac{{\frac{{2\pi \,rad}}{{60\,s}}}}{{\frac{{2\pi \,rad}}{{12 \times 60 \times 60\,s}}}} = 720\)
