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 -

Options

A. `-8hatim//s`
B. `-9hatim//s`
C. `-6hatim//s`
D. None of these

Answer

2

Explanation

`(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`