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Figure shows a concave mirror of focal l...


Figure shows a concave mirror of focal length 20 cm. A point object P is oscillating along te principle axis of the mirror. Position co-ordinates of image at any time `t` is given by:
`x_(i)=40+20sin(2t+(5pi)/(6))`
Here x is in cm and t is in positive.

A

a. Speed of the object at `t=0` is `40sqrt(3)cm//s`

B

b. speed of the object at `t=0` is `(80sqrt(3))/(9)cm//s`

C

c. if we start observing at `t=0` minimum time `t` at which object & image will cross each other is `(pi)/(12)` s

D

d. if we start observing at `t=0`, minimum time `t` at which object & imega will cross each other is `(pi)/(6)s`

Text Solution

Verified by Experts

The correct Answer is:
B, C
At `t=0` image distance `v=-50cm`
velocity of image `V_(I)=-20sqrt(3)cm//s`
`V_(I)=-m^(2).v_(0)`
`20sqrt(3)=((f-v)/(f))^(2)V_(0)`
`20sqrt(3)=-((-20+50)/(-20))^(2)V_(0)`
`20sqrt(3)=-(9)/(4)V_(0)`
`V_(0)=80(sqrt(3))/(9)cm//s`
Object & image will cross each other at centre of curvature i.e., when `x_(i)=40`
`2t+(5pi)/(6)=pi`
`2t+(pi)/(6)impliest=(pi)/(42)`s
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