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Q.

A linear object AB is placed along the axis of a concave mirror. The object is moving towards the mirror with speed u. The speed of the image of the point A is 4u and the speed of the image of B is also 4u but in opposite direction. If the centre of the line AB is at a distance L from the mirror then find out the length of the object.

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a

3L/2

b

5L/3

c

L

d

None of these

answer is C.

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Detailed Solution

For concave mirror, if x and y are object distance and image distance, respectively, we have−1x−1y=−1f⇒1x+1y=−1f ⇒−1x2dxdt−1y2dydt=0⇒VxVy=x2y2For, VxVy=14,xy=±2For x/y=2, we get x=3f/2 [for point A] and for x/y=−2, we get x=f/2 [for point B].As the middle point happens to be focus of the mirror, we get f=L.

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A linear object AB is placed along the axis of a concave mirror. The object is moving towards the mirror with speed u. The speed of the image of the point A is 4u and the speed of the image of B is also 4u but in opposite direction. If the centre of the line AB is at a distance L from the mirror then find out the length of the object.