| A ball is rolled over a horizontal ground making an angle of \[45{}^\circ \] with a mirror wall in an art gallery |
 |
| If velocity of ball is \[1m{{s}^{-1}}\], then velocity of image of ball with respect to ball will be |
A) \[\sqrt{2}m{{s}^{-1}}\]
B) \[\sqrt{3}m{{s}^{-1}}\]
C) \[\frac{1}{\sqrt{2}}m{{s}^{-1}}\]
D) \[\frac{1}{\sqrt{3}}m{{s}^{-1}}\]
Correct Answer: A
Solution :
| Velocity components of object and image are as shown below. |
| Clearly,\[{{\upsilon }_{object}}=\upsilon \left( -\frac{1}{\sqrt{2}}\overset{\hat{\ }}{\mathop{i}}\,+\frac{1}{\sqrt{2}}\overset{\hat{\ }}{\mathop{j}}\, \right)\] |
| And \[{{\upsilon }_{image}}=\upsilon \left( -\frac{1}{\sqrt{2}}\overset{\hat{\ }}{\mathop{i}}\,+\frac{1}{\sqrt{2}}\overset{\hat{\ }}{\mathop{j}}\, \right)\]b |
| Relative velocity of image with respect to |
| abject is \[{{\upsilon }_{rel}}={{\upsilon }_{image}}-{{\upsilon }_{object}}\] |
| \[=\sqrt{2}\,\,\upsilon \hat{i}=\sqrt{2}\,\hat{i}\,m{{s}^{-1}}\] |
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