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Question

# A car is fitted with a convex side view mirror of focal length 20 cm. A second car 2.8 m behind the first car is overtaking the first car at a relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first car will be :

A
115 m/s
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B
120 m/s
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C
125 m/s
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D
130 m/s
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Solution

## The correct option is A 115 m/sFor the given convex mirror, u=−2.8 m=−280 cm, f=+20 cm Using mirror formula, 1v−1280=120 ⇒1v=356 ⇒v=563 cm So, m=−vu=−563−280=115 Also, velocity of the image when the object is moving along the principal axis, vi,m=−m2vo,m ⇒vi,m=−(115)2×15=−115 m/s Hence, the speed of the image of the second car as seen in the mirror of the first car will be : 115 m/s. Why this question?Tips: As relative velocity is given, thus we canassume mirror of first car to be in rest and can applyformula with sign convention.

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