Image of an object approaching a convex mirror of radius of curvature 20m slong its optical axis is observed to move from `(25)/(3)`m to `(50)/(7)`m in 30 seconds. What is the speed of the object in km per hour?

Options

A. 5 km/h
B. 4 km/h
C. 3 km/h
D. 2 km/h

Answer

C

Explanation

For the convex mirror, `f=(R )/(2)=10m`
(f is +ve, v is +ve and u is -ve)
In the first case, `(1)/(v)+(1)/(u)=(1)/(f)`
`therefore (1)/(u_(1))=(1)/(f)-(1)/(v_(1))=(1)/(10)-(1)/(25//3)=(1)/(10)-(3)/(25)`
`therefore (1)/(u_(1))= - (1)/(50) therefore u_(1)= -50 cm`
and the second case,
`therefore (1)/(u_(2))=(1)/(10)-(1)/((50//7))=(1)/(10)-(7)/(50)`
`=(-2)/(50)= -(1)/(25)`
`therefore u_(2)=-25 cm`
` therefore` Object moves through 25 cm in 30 s.
`therefore v=(25)/(30) m//s=(25)/(30)xx(18)/(5)=3` km/hour