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Question

An object is initially at a distance of 200 cm from a plane mirror. If the mirror approaches the object at a speed of 15 cm/s, then after 8 sec the distance between object and its image will be

A
120 cm
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B
160 cm
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C
170 cm
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D
30 cm
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Solution

The correct option is B 160 cm

Initial distance between object and image,
OI=2×200=400 cm
Relative velocity along perpendicular to the plane
vo,m=vi,m
Taking leftwards as +ve direction,
vovm=(vivm)
015=vi+15
vi=+30 cm/s
In Δt=8 s, the distance travelled/covered by image will be,
S=vi×Δt=30×8=240 cm
Thus, the distance between object and image will be,
OI=OIS
OI=400240=160 cm, (After 8 sec).

Alternative:
Initial distance between object and mirror, OM=200 cm
Distance covered by mirror in 8 s, =15×8=120 cm
Distance between object and mirror, OM=200120=80 cm
Therefore distance between object and its image, OI=2×80=160 cm

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