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Q.

An object and a concave mirror of focal length f=10cm both move along the principal axis of the mirror with constant speeds. The object moves with speed V0=15cms1 towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at a given moment is denoted by u. When u=30cm, the speed of the mirror Vm is such that the image is instantaneously at rest with respect to the laboratory frame, and the object forms a real image. The magnitude of Vm is _______ cms1

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Detailed Solution

As shown in figure below, we consider mirror velocity to be on the right side
 Question Image
Using mirror formula, position of image is obtained as
u=30cm      f=10cm                  v=f0uf=15cm
Magnification of object is given as  m=12
Relative velocity of image with respect to mirror is given as
  VIM=m2VOM=14VOM
As image is at instantaneous rest, we use V1=0

VM=14(V0VM)           VM=15V0=3cm/s

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An object and a concave mirror of focal length f=10cm both move along the principal axis of the mirror with constant speeds. The object moves with speed V0=15cms−1 towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at a given moment is denoted by u. When u=30cm, the speed of the mirror Vm is such that the image is instantaneously at rest with respect to the laboratory frame, and the object forms a real image. The magnitude of Vm is _______ cms−1