Question

# A plane mirror and an object approach each other with speeds of 5 msâˆ’1 and 10 msâˆ’1 respectively. What will be the speed of the image w.r.t. the stationary observer?

A

5 ms1

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B

15 ms1

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C

20 ms1

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D

25 ms1

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Solution

## The correct option is D 25 ms−1 Given: Speed of object, uo=5 ms−1 Speed of mirror, um=10 ms−1 Mirror and object are approaching each other. To find: Speed of image Procedure: Let initial position of object be at xoi=0 Let initial position of mirror be at xmi=u Object distance equals the image distance. Hence, initial position of image is xii=2u Distance is the product of speed and time. After time t, Position of object will be: xof=xoi+uot=5t Position of mirror will be: xmf=xmi−uft=u−10t Let the final position of image be xif Using object distance equals image distance after time t. xif−xmf=xmf−xof xif=2u−25t Distance moved by image in time t is: si=xif−xii si=−25t Speed is the ratio of distance and time. Speed of the image is: vi=sit=−25 Negative sign appears because image is moving leftwards. Hence, speed of image is 25 ms−1

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