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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, ⇒vo−vm=−(vi−vm) ⇒0−15=−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′=OI−S ⇒OI′=400−240=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′=200−120=80 cm Therefore distance between object and its image, OI′=2×80=160 cm

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