Question

# A concave mirror of radius of curvature R is moving towards object of mass m with constant velocity V0. Mirror make elastic collision with object at pole at t = 0. Mass of mirror is very large compare to mass of object. Column-1 Shown time, Column-2 shows speed of image of object, column-3 shows distance of image from pole of mirror at given time (D1) Column 1Column 2Column 3(I)t=R4V0(i)V1=89V0(P)D1=3R(II)t=3R5V0(ii)V1=24V0(Q)D1=R2(III)t=RV0(iii)V1=3V0(R)D1=23R(IV)t=2RV0(iv)V1=0(S)D1=R Which of the following correctly matched  (II) (iv) (S)(III) (iii) (P)(I) (ii) (P)(I) (iii) (Q)

Solution

## The correct option is D (I) (iii) (Q) To perceive this we can go on the reference of the mirror, then it will be analogous to the situation where a ball hits a wall elastically. at t=R4V0u=−R4 V=ufu−f(−R4)(−R2)−R4+R2=R2  V1=−(m)2V0+V0=−(2)2V+V=−3V Here m is velocity magnification i.e v2u2 Now, at t=3R5V0 u=−3R5 V=4fu−f  V=−3R D1=|V|=3R V1=−(5)2V0+V0=−24V0 at t=RV0u=−R V=−R  D1=|V|=R V1=−(1)2V0+V0=0 at t=2RV0  u=−2R V=ufu−f=23R  M=−Vu=13 V1=−(13)2  V0+V0=89V0

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