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Question

An object is placed in front of a convex mirror at a distance of 60 m from its pole. Object starts moving towards the mirror at 20 ms1. Find the average speed of the image for a time interval of 2 s if the focal length of the mirror is 20 m.


A

0.568 ms1

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B

1 ms1

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C

3 ms1

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D

2.5 ms1

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Solution

The correct option is D

2.5 ms1


Given:
Initial object distance, u=60 m
Speed of object, vo=20 ms1
Focal length, f=20 m
Time interval, t=2 s

Applying mirror formula to find the initial position of the image v:
1v+1u=1f
1v+160=120
v=15 m

Distance travelled by the object is the product of speed and time.
so=vot
so=20×2=40 m

Therefore, now the object distance:
uf=u+so=60+40=20 m

Applying mirror formula to find the final position of the image vf:
1vf+1uf=1f
1vf+120=120
vf=10 m

Average speed is the ratio of total distance travelled to the total time taken.
Average speed of the image:
vi=vvft
vi=15102=2.5 ms1


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