- 1(current)
Q. No.A particle moves uniformly in a circle of radius \(R\) with a speed \(v.\) When it covers a semi-circle (for the first time), its average velocity is:
| 1. | \(v\) | 2. | \(\Large\frac{v}{2}\) |
| 3. | \(\Large\frac{v}{\pi}\) | 4. | \(\Large\frac{2v}{\pi}\) |
Subtopic: Â Speed & Velocity |
 59%
Level 3: 35%-60%
Hints
Consider a square carrom board \(ABCD\) of size \({3~ \text{ft}} \times 3~\text{ft}. \) A piece moves 'from' pocket \(A\) (close from a pocket), strikes side \(BC\) and then side \(AD\), and reaches pocket \(C\). If the piece is reflected perfectly from each side, then the ratio of the \(x,y\) components of velocity is given by \(\dfrac{v_x}{v_y}=\)
| 1. | \(2\) | 2. | \(\dfrac{1}{2}\) |
| 3. | \(3\) | 4. | \(\dfrac{1}{3}\) |
Subtopic: Â Speed & Velocity |
 56%
Level 3: 35%-60%
Hints
\(ABCD\) is a smooth, horizontal, square board of dimension \(2~\text m\times2~\text m.\) A small ball, lying at the centre \(O,\) is given an initial velocity \(\vec v\) so that it rebounds elastically off the edges \(AB\) and \(CD,\) and reaches the corner \(B.\) The time required for the entire motion is \(2~\text s.\) The axes are shown in the figure.
The average velocity of the ball is:
The average velocity of the ball is:
| 1. | \(\dfrac{1}{2}\left(\hat i+\hat j\right)~\text{m/s}\) | 2. | \(2\left(\hat i+\hat j\right)~\text{m/s}\) |
| 3. | \(\sqrt2\left(\hat i+\hat j\right)~\text{m/s}\) | 4. | \(\dfrac{1}{\sqrt2}\left(\hat i+\hat j\right)~\text{m/s}\) |
Subtopic: Â Speed & Velocity |
 58%
Level 3: 35%-60%
Hints
\(ABCD\) is a smooth, horizontal, square board of dimension \(2~\text m\times2~\text m.\) A small ball, lying at the centre \(O,\) is given an initial velocity \(\vec v\) so that it rebounds elastically off the edges \(AB\) and \(CD,\) and reaches the corner \(B.\) The time required for the entire motion is \(2~\text s.\) The axes are shown in the figure.
The initial velocity of the ball is:
The initial velocity of the ball is:
| 1. | \(\dfrac{1}{2}\left(\hat i+\hat j\right)~\text{m/s}\) | 2. | \(\dfrac{1}{2}\left(\hat i+3\hat j\right)~\text{m/s}\) |
| 3. | \(\dfrac{1}{2}\left(\hat i+5\hat j\right)~\text{m/s}\) | 4. | \(\dfrac{1}{2}\left(\hat i+6\hat j\right)~\text{m/s}\) |
Subtopic: Â Speed & Velocity |
Level 3: 35%-60%
Hints
\(ABCD\) is a smooth, horizontal, square board of dimension \(2~\text m\times2~\text m.\) A small ball, lying at the centre \(O,\) is given an initial velocity \(\vec v\) so that it rebounds elastically off the edges \(AB\) and \(CD,\) and reaches the corner \(B.\) The time required for the entire motion is \(2~\text s.\) The axes are shown in the figure.
The average speed of the ball is (during the motion):
The average speed of the ball is (during the motion):
| 1. | \(\dfrac{1}{\sqrt2}~\text{m/s}\) | 2. | \(\dfrac{\sqrt{26}}{2}~\text{m/s}\) |
| 3. | \(\dfrac{\sqrt{10}}{2}~\text{m/s}\) | 4. | \(\sqrt2~\text{m/s}\) |
Subtopic: Â Speed & Velocity |
Level 3: 35%-60%
Hints
- 1(current)
Q. No.
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