04. Circular Motion : Uniform Circular Motion, Dynamic Circular Motion
Motion in Plane

144048 The overbridge of a canal is in the form of a concave circular arc of radius ' \(r\) '. The thrust at the lowest point is \((m=\) mass of the vehicle, \(v=\) velocity of the vehicle, \(g=\) acceleration due to gravity).

1 \(\mathrm{mg} \div \mathrm{mv}^{2} / \mathrm{r}\)
2 \(\left(\mathrm{mg}+\frac{\mathrm{mv}^{2}}{\mathrm{r}}\right)\)
3 \(\left(\mathrm{mg}-\frac{\mathrm{mv}}{\mathrm{r}}\right)\)
4 \(\mathrm{mg} \times \frac{\mathrm{mv}^{2}}{\mathrm{r}}\)
Motion in Plane

144049 A particle of mass 4 gram moves along a circle of radius \(\frac{10^{2}}{2 \pi} \mathrm{cm}\) with constant tangential acceleration. After beginning of the motion, by the end of second revolution, the kinetic energy of the particle becomes \(18 \times 10^{-5} \mathrm{~J}\). Magnitude of tangential acceleration is

1 \(2.25 \times 10^{-6} \mathrm{~m} / \mathrm{s}^{2}\)
2 \(2.25 \times 10^{-5} \mathrm{~m} / \mathrm{s}^{2}\)
3 \(2.25 \times 10^{-4} \mathrm{~m} / \mathrm{s}^{2}\)
4 \(2.25 \times 10^{-3} \mathrm{~m} / \mathrm{s}^{2}\)
Motion in Plane

144050 A coin kept at a distance ' \(r_{1}\) ' \(\mathrm{cm}\) from the axis of rotation of a turn table, just begins to slip when the turntable rotates at an angular speed of ' \(\omega_{1}\) ' \(\mathrm{rad} / \mathrm{s}\). If this distance is tripled, then at what angular speed of the turntable, will the coin begin to slip ?

1 \(3 \omega_{1} \mathrm{rad} / \mathrm{s}\)
2 \(\sqrt{3} \omega_{1} \mathrm{rad} / \mathrm{s}\)
3 \(\frac{\omega_{1}}{\sqrt{3}} \mathrm{rad} / \mathrm{s}\)
4 \(\frac{\omega_{1}}{3} \mathrm{rad} / \mathrm{s}\)
Motion in Plane

144051 The real force ' \(F\) ' acting on a particle of mass ' \(m\) ' performing circular motion acts along the radius of circle ' \(r\) ' and is directed towards the centre of circle. The square root of magnitude of such force is \((\tau=\) periodic time \()\)

1 \(\frac{2 \pi}{\mathrm{T}} \sqrt{\mathrm{mr}}\)
2 \(\frac{T^{2} m r}{4 \pi}\)
3 \(\frac{2 \pi \mathrm{T}}{\sqrt{\mathrm{mr}}}\)
4 \(\frac{\mathrm{Tmr}}{4 \pi}\)
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Motion in Plane

144048 The overbridge of a canal is in the form of a concave circular arc of radius ' \(r\) '. The thrust at the lowest point is \((m=\) mass of the vehicle, \(v=\) velocity of the vehicle, \(g=\) acceleration due to gravity).

1 \(\mathrm{mg} \div \mathrm{mv}^{2} / \mathrm{r}\)
2 \(\left(\mathrm{mg}+\frac{\mathrm{mv}^{2}}{\mathrm{r}}\right)\)
3 \(\left(\mathrm{mg}-\frac{\mathrm{mv}}{\mathrm{r}}\right)\)
4 \(\mathrm{mg} \times \frac{\mathrm{mv}^{2}}{\mathrm{r}}\)
Motion in Plane

144049 A particle of mass 4 gram moves along a circle of radius \(\frac{10^{2}}{2 \pi} \mathrm{cm}\) with constant tangential acceleration. After beginning of the motion, by the end of second revolution, the kinetic energy of the particle becomes \(18 \times 10^{-5} \mathrm{~J}\). Magnitude of tangential acceleration is

1 \(2.25 \times 10^{-6} \mathrm{~m} / \mathrm{s}^{2}\)
2 \(2.25 \times 10^{-5} \mathrm{~m} / \mathrm{s}^{2}\)
3 \(2.25 \times 10^{-4} \mathrm{~m} / \mathrm{s}^{2}\)
4 \(2.25 \times 10^{-3} \mathrm{~m} / \mathrm{s}^{2}\)
Motion in Plane

144050 A coin kept at a distance ' \(r_{1}\) ' \(\mathrm{cm}\) from the axis of rotation of a turn table, just begins to slip when the turntable rotates at an angular speed of ' \(\omega_{1}\) ' \(\mathrm{rad} / \mathrm{s}\). If this distance is tripled, then at what angular speed of the turntable, will the coin begin to slip ?

1 \(3 \omega_{1} \mathrm{rad} / \mathrm{s}\)
2 \(\sqrt{3} \omega_{1} \mathrm{rad} / \mathrm{s}\)
3 \(\frac{\omega_{1}}{\sqrt{3}} \mathrm{rad} / \mathrm{s}\)
4 \(\frac{\omega_{1}}{3} \mathrm{rad} / \mathrm{s}\)
Motion in Plane

144051 The real force ' \(F\) ' acting on a particle of mass ' \(m\) ' performing circular motion acts along the radius of circle ' \(r\) ' and is directed towards the centre of circle. The square root of magnitude of such force is \((\tau=\) periodic time \()\)

1 \(\frac{2 \pi}{\mathrm{T}} \sqrt{\mathrm{mr}}\)
2 \(\frac{T^{2} m r}{4 \pi}\)
3 \(\frac{2 \pi \mathrm{T}}{\sqrt{\mathrm{mr}}}\)
4 \(\frac{\mathrm{Tmr}}{4 \pi}\)
Motion in Plane

144048 The overbridge of a canal is in the form of a concave circular arc of radius ' \(r\) '. The thrust at the lowest point is \((m=\) mass of the vehicle, \(v=\) velocity of the vehicle, \(g=\) acceleration due to gravity).

1 \(\mathrm{mg} \div \mathrm{mv}^{2} / \mathrm{r}\)
2 \(\left(\mathrm{mg}+\frac{\mathrm{mv}^{2}}{\mathrm{r}}\right)\)
3 \(\left(\mathrm{mg}-\frac{\mathrm{mv}}{\mathrm{r}}\right)\)
4 \(\mathrm{mg} \times \frac{\mathrm{mv}^{2}}{\mathrm{r}}\)
Motion in Plane

144049 A particle of mass 4 gram moves along a circle of radius \(\frac{10^{2}}{2 \pi} \mathrm{cm}\) with constant tangential acceleration. After beginning of the motion, by the end of second revolution, the kinetic energy of the particle becomes \(18 \times 10^{-5} \mathrm{~J}\). Magnitude of tangential acceleration is

1 \(2.25 \times 10^{-6} \mathrm{~m} / \mathrm{s}^{2}\)
2 \(2.25 \times 10^{-5} \mathrm{~m} / \mathrm{s}^{2}\)
3 \(2.25 \times 10^{-4} \mathrm{~m} / \mathrm{s}^{2}\)
4 \(2.25 \times 10^{-3} \mathrm{~m} / \mathrm{s}^{2}\)
Motion in Plane

144050 A coin kept at a distance ' \(r_{1}\) ' \(\mathrm{cm}\) from the axis of rotation of a turn table, just begins to slip when the turntable rotates at an angular speed of ' \(\omega_{1}\) ' \(\mathrm{rad} / \mathrm{s}\). If this distance is tripled, then at what angular speed of the turntable, will the coin begin to slip ?

1 \(3 \omega_{1} \mathrm{rad} / \mathrm{s}\)
2 \(\sqrt{3} \omega_{1} \mathrm{rad} / \mathrm{s}\)
3 \(\frac{\omega_{1}}{\sqrt{3}} \mathrm{rad} / \mathrm{s}\)
4 \(\frac{\omega_{1}}{3} \mathrm{rad} / \mathrm{s}\)
Motion in Plane

144051 The real force ' \(F\) ' acting on a particle of mass ' \(m\) ' performing circular motion acts along the radius of circle ' \(r\) ' and is directed towards the centre of circle. The square root of magnitude of such force is \((\tau=\) periodic time \()\)

1 \(\frac{2 \pi}{\mathrm{T}} \sqrt{\mathrm{mr}}\)
2 \(\frac{T^{2} m r}{4 \pi}\)
3 \(\frac{2 \pi \mathrm{T}}{\sqrt{\mathrm{mr}}}\)
4 \(\frac{\mathrm{Tmr}}{4 \pi}\)
Motion in Plane

144048 The overbridge of a canal is in the form of a concave circular arc of radius ' \(r\) '. The thrust at the lowest point is \((m=\) mass of the vehicle, \(v=\) velocity of the vehicle, \(g=\) acceleration due to gravity).

1 \(\mathrm{mg} \div \mathrm{mv}^{2} / \mathrm{r}\)
2 \(\left(\mathrm{mg}+\frac{\mathrm{mv}^{2}}{\mathrm{r}}\right)\)
3 \(\left(\mathrm{mg}-\frac{\mathrm{mv}}{\mathrm{r}}\right)\)
4 \(\mathrm{mg} \times \frac{\mathrm{mv}^{2}}{\mathrm{r}}\)
Motion in Plane

144049 A particle of mass 4 gram moves along a circle of radius \(\frac{10^{2}}{2 \pi} \mathrm{cm}\) with constant tangential acceleration. After beginning of the motion, by the end of second revolution, the kinetic energy of the particle becomes \(18 \times 10^{-5} \mathrm{~J}\). Magnitude of tangential acceleration is

1 \(2.25 \times 10^{-6} \mathrm{~m} / \mathrm{s}^{2}\)
2 \(2.25 \times 10^{-5} \mathrm{~m} / \mathrm{s}^{2}\)
3 \(2.25 \times 10^{-4} \mathrm{~m} / \mathrm{s}^{2}\)
4 \(2.25 \times 10^{-3} \mathrm{~m} / \mathrm{s}^{2}\)
Motion in Plane

144050 A coin kept at a distance ' \(r_{1}\) ' \(\mathrm{cm}\) from the axis of rotation of a turn table, just begins to slip when the turntable rotates at an angular speed of ' \(\omega_{1}\) ' \(\mathrm{rad} / \mathrm{s}\). If this distance is tripled, then at what angular speed of the turntable, will the coin begin to slip ?

1 \(3 \omega_{1} \mathrm{rad} / \mathrm{s}\)
2 \(\sqrt{3} \omega_{1} \mathrm{rad} / \mathrm{s}\)
3 \(\frac{\omega_{1}}{\sqrt{3}} \mathrm{rad} / \mathrm{s}\)
4 \(\frac{\omega_{1}}{3} \mathrm{rad} / \mathrm{s}\)
Motion in Plane

144051 The real force ' \(F\) ' acting on a particle of mass ' \(m\) ' performing circular motion acts along the radius of circle ' \(r\) ' and is directed towards the centre of circle. The square root of magnitude of such force is \((\tau=\) periodic time \()\)

1 \(\frac{2 \pi}{\mathrm{T}} \sqrt{\mathrm{mr}}\)
2 \(\frac{T^{2} m r}{4 \pi}\)
3 \(\frac{2 \pi \mathrm{T}}{\sqrt{\mathrm{mr}}}\)
4 \(\frac{\mathrm{Tmr}}{4 \pi}\)