Q. No.The angular speed of seconds needle in a mechanical watch is:
(1) rad/s
(2) 2π rad/s
(3) π rad/s
(4) rad/s
| 1. | \(6 \hat{i}+2 \hat{j}-3 \hat{k} \) |
| 2. | \(-18 \hat{i}-13 \hat{j}+2 \hat{k} \) |
| 3. | \(4 \hat{i}-13 \hat{j}+6 \hat{k}\) |
| 4. | \(6 \hat{i}-2 \hat{j}+8 \hat{k}\) |
A particle moves with constant speed \(v\) along a circular path of radius \(r\) and completes the circle in time \(T\). The acceleration of the particle is:
1. \(2\pi v / T\)
2. \(2\pi r / T\)
3. \(2\pi r^2 / T\)
4. \(2\pi v^2 / T\)
If ar and at represent radial and tangential accelerations, the motion of a particle will be uniformly circular if:
1. ar = 0 and at = 0
2. ar = 0 but at \(\neq\) 0
3. ar \(\neq\) 0 but at = 0
4. ar \(\neq\) 0 and at \(\neq\) 0
1. \(3.14~\text{m/s}\)
2. \(2.0~\text{m/s}\)
3. \(1.0~\text{m/s}\)
4. zero
A stone tied to the end of a string of \(1\) m long is whirled in a horizontal circle with a constant speed. If the stone makes \(22\) revolutions in \(44\) s, what is the magnitude and direction of acceleration of the stone?
| 1. | \(\dfrac{\pi^2}{4}\) ms–2 and direction along the radius towards the center |
| 2. | \(\pi^2\) ms–2 and direction along the radius away from the center |
| 3. | \(\pi^2 \) ms–2 and direction along the radius towards the center |
| 4. | \(\pi^2\) ms 2 and direction along the tangent to the circle |
If the equation for the displacement of a particle moving on a circular path is given by \(\theta = 2t^3 + 0.5\) where \(\theta\) is in radians and \(t\) in seconds, then the angular velocity of the particle after \(2\) sec from its start is:
1. \(8\) rad/sec
2. \(12\) rad/sec
3. \(24\) rad/sec
4. \(36\) rad/sec
For a particle in a non-uniform accelerated circular motion
(1) Velocity is radial and acceleration is transverse only
(2) Velocity is transverse and acceleration is radial only
(3) Velocity is radial and acceleration has both radial and transverse components
(4) Velocity is transverse and acceleration has both radial and transverse components
The coordinates of a moving particle at any time \(t\) are given by \(x= \alpha t^3\) and \(y = \beta t^3.\) The speed of the particle at a time \(t\) is given by:
| 1. | \(\sqrt{\alpha^{2} + \beta^{2}}\) | 2. | \(3t \sqrt{\alpha^{2} + \beta^{2}}\) |
| 3. | \(3t^{2} \sqrt{\alpha^{2} +\beta^{2}}\) | 4. | \(t^{2} \sqrt{\alpha^{2} +\beta^{2}}\) |
A particle moves in a circular path with decreasing speed. Choose the correct statement.
(1) Angular momentum remains constant
(2) Acceleration () is towards the center
(3) Particle moves in a spiral path with decreasing radius
(4) The direction of angular momentum remains constant
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