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A point object moves in + x-direction with v= 1 m/s along the principal axis of the concave mirror of focal length f=10 m. When the mirror moves with a velocity `V_(m)=-hati` m/s and the object is at a distance of p=15 m, the speed of the image is - A. `-8hatim//s`B. `-9hatim//s`C. `-6hatim//s`D. None of these |
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Answer» Correct Answer - 2 `(1)/(p)+(1)/(q)=(1)/(f)or(-dp//dt)/(p^(2))-(dq//dt)/(q^(2))=0` `or- overset(-)v_(om//p^(2))=overset(-)V_(im//q^(2))` `oroverset(-)v_(im)=-((q)/(p))^(2)" "overset(-)V_("om")` If p=15, `(1)/(q)=(1)/(f)-(1)/(p)=(1)/(10)-(1)/(15)` `or q=30 m. Then, q//p=30//15=2.Hence` `overset(-)v_("im")=-(2)^(2)V_("om")` or `overset(-)V_(i)=overset(-)V_("im")+overset(-)V_("m")=-(2)^(2)" "overset(-)V_("om")+overset(-)V_("m")` `-4[(hati)-(-hati)]+(hati)=-9(hati)m//s` |
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