An object moving at a speed of 5m/s towards a concave mirror of focal length f=1 m is at a distance of 9m. The average speed of the image is

Options

A. `(1)/(5)`m/s
B. `(1)/(10)`m/s
C. `(5)/(9)`m/s
D. `(2)/(5)`m/s

Answer

A

Explanation

`u= - 9 m, f = -1m`
`(1)/(v) = (1)/(f) - (1)/(u) = (1)/(-1) + (1)/(9) = (-8)/(9) rarr v = (-9)/(8)` m
speed of object = 5 m/s
After 1 sec the position of image
u = - 9 + 5 = -4 m
`(1)/(v) = (1)/(f) - (1)/(u) = (1)/(-1) + (1)/(4) = (-3)/(4) rArr v. = (-4)/(3) `m
distance move by image in 1 sec
`=v - v. = (-9)/(8) + (4)/(3) = (-27+ 32)/(24)`
`= (5)/(24) = (1)/(4.8) = (1)/(5)`
Average speed of the image `= (1)/(5) `m/s.