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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/s
For the given convex mirror,
u=2.8 m=280 cm, f=+20 cm
Using mirror formula,
1v1280=120
1v=356
v=563 cm
So, m=vu=563280=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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