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Question

# A motor car is fitted with a convex driving mirror of focal length 20cm. A second motor car 2.8m behind the first car is overtaking speed of 15 msâˆ’1. The speed of the image of the second car as seen in the mirror of the first is :

A
110ms1
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B
115ms1
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C
10ms1
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D
15ms1
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Solution

## The correct option is A 115ms−1Givenfocal length f=20cmObject distance, u=2.8m=280cmSpeed of object, v0=15m/sfrom mirror formula1f=1v+1u....(1)differentiating on b/s wrt t0=−1v2dvdt−1u2dudt⇒ dvdt=−[v2u2dudt]...(2)Also from (1)120=1v−12801v=15280v=28015cmPutting value in (2)⇒ dvdt=vi,dudt=v0⇒ vi=−[28015×280]215m/svi=−115m/sSpeed =115m/s

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