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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 ms1. 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 115ms1
Given

focal length f=20cm

Object distance, u=2.8m=280cm

Speed of object, v0=15m/s

from mirror formula

1f=1v+1u....(1)

differentiating on b/s wrt t

0=1v2dvdt1u2dudt

dvdt=[v2u2dudt]...(2)

Also from (1)

120=1v1280

1v=15280

v=28015cm

Putting value in (2)

dvdt=vi,dudt=v0

vi=[28015×280]215m/s

vi=115m/s

Speed =115m/s

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