Question

An object and a concave mirror of focal length $f=10$$\text{cm}$ both move along the principal axis of the mirror with constant speeds. The object moves with speed $V_0=15$${\text{cms}}^{–1}$ towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at a given moment is denoted by $u$. When $u=30$$\text{cm}$, the speed of the mirror $V_m$ is such that the image is instantaneously at rest with respect to the laboratory frame, and the object forms a real image. The magnitude of $V_m$ is ${\text{cms}}^{–1}$.

• A. 3
• B. 3.00
• C. 3.0

Answer 1

Answer: (A), (B), (C)

Given:
focal length $f=10$$\text{cm}$
object speed $V_0=15$${\text{cms}}^{–1}$ towards the mirror
$u=30$$\text{cm}$,
As we know, $V_l-V_m=-m^2(V_0-V_m)\text{where}m=\frac{f}{f-u}=-\frac{1}{2}$
$\Rightarrow V_l=V_m-m^2(V_0-V_m);(1+m)V_m=m^2{V}_0$
$\Rightarrow (1+\frac{1}{4})V_m=\frac{1}{4}\times 15$
$\Rightarrow V_m=3$