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Question

# Find the velocity of the image of object O with respect to ground in the given figure. The velocities of the object and the mirror w.r.t ground are given.

A
54 cm/s towards the mirror
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B
74 cm/s towards the mirror
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C
74 cm/s away from the mirror
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D
79 cm/s away from the mirror
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Solution

## The correct option is C 74 cm/s away from the mirrorFor the given concave mirror, u=−30 cm, f=−10 cm Relative velocity of object with respect to mirror, vom=vog−vmg=2−(−1)=3 cm/s Using mirror formula, 1v−130=−110 ⇒1v=−115 ⇒v=−15 cm So, m=−vu=−(−15)−30=−12 Also, velocity of the image when the object is moving along the principal axis, vim=−m2vom ⇒vim=−(−12)2×3=−34 cm/s Now, the velocity of the image with respect to ground, vig=vim+vmg ⇒vig=−34−1=−74 cm/s Since, the image is formed on the left side of the mirror (v=−ve) and the image is moving in the left direction (vim=−ve), we can say that velocity of the image is away from the mirror. Hence, the velocity of the image with respect to ground will be 74 cm/s away from the mirror. Why this question ?It provides unique blend of concept of relativemotion and mirror formula.Tips: Apply the formula of image velocity w.r.t mirrorand be cautious in sign convention.

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