Radial & Tangential Acceleration for Non Uniform Circular Motion

Q. An object is tied to a string and rotated in a vertical circle of radius $r$. Constant speed $\left(v\right)$ is maintained along the trajectory. If $\frac{T_{max}}{T_{min}}=2$, then $\frac{v^2}{rg}=$

Q.

A particle moves in a circle of radius 25 cm at two revolutions per second. The acceleration of the particle in $m/s^2$ is

1. ${\pi }^2$

2. $8{\pi }^2$

3. $2{\pi }^2$

4. $4{\pi }^2$

Q.

A car travels north with a uniform velocity. It goes over a piece of mud which sticks to the tyre. The particles of the mud, as it leaves the ground are thrown

1. Vertically upwards

2. Towards south

3. Vertically inwards

4. Towards north

Q.

A proton of mass $1.6\times {10}^{-27}$ kg goes round in a circular orbit of radius 0.10 m under a centripetal force of $4\times {10}^{-13}N$. then the frequency of revolution of the proton is about

1. $0.08\times {10}^{8}cyclespersec$

2. $12\times {10}^{8}cyclespersec$

3. $8\times {10}^{8}cyclespersec$

4. $4\times {10}^{8}cyclespersec$

Q. The bob of the pendulum shown in the figure describes an arc of a circle in a vertical plane. If the tension in the cord is $3$ times of the weight of the bob for the position shown, the velocity of the bob at this position is

1. $6.47\text{m/s}$
2. $10\text{m/s}$
3. $0\text{m/s}$
4. $15\text{m/s}$

Q. A $1\text{kg}$ stone at the end of a $1\text{m}$ long string is whirled in a vertical circle at a constant speed of $4\text{m/s}$. The tension in the string is $6\text{N}$ when the stone is (Take $g=10{\text{m/s}}^2$)

1. At the top of the circle.
2. At the bottom of the circle.
3. Half way down
4. None of above

Q. A small stone of mass $200\text{g}$ is tied to one end of a string of length $80\text{cm}$. Holding the other end in the hand, the stone is whirled in a vertical circle. What is the minimum speed that needs to be imparted at the lowest point such that the stone is just able to complete the vertical circle?(Take $g=10\text{m}/s^2$)

1. $4\text{m/s}$
2. $5.13\text{m/s}$
3. $6.32\text{m/s}$
4. $7\text{m/s}$

Q. A stone of mass $1\text{kg}$ tied to a light string of length $\frac{10}{3}\text{m}$ is whirled in a vertical circle. If the ratio of the maximum tension to minimum tension is 4 and $g=10{\text{m/s}}^2$, then the speed of the stone at the highest point of the circle is

1. $20\text{m/s}$
2. $10\text{m/s}$
3. $5\text{m/s}$
4. $0\text{m/s}$

Q. The bob of a pendulum at rest is given a sharp hit to impart a horizontal velocity $u=\sqrt{10gl}$, where $l$ is the length of the pendulum. Then, the tension in the string when it is horizontal is $xmg$ where $x=$

Q. The bob of a pendulum at rest is given a sharp hit to impart a horizontal velocity $u=\sqrt{10gl}$, where $l$ is the length of the pendulum. Find the velocity of the bob when the string is horizontal.

1. $\sqrt{2gl}$
2. $\sqrt{4gl}$
3. $\sqrt{6gl}$
4. $\sqrt{8gl}$