Moving Mirror

Q. 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 ${\text{cms}}^{–1}$.

Q. What is the velocity (in cm/s) of image in situation shown below? Object moves with velocity 10 cm/s and mirror moves with velocity 2 cm/s as shown.

1. 2 cm/s
2. 0 cm/s
3. 4 cm/s
4. 1 cm/s

Q. What is the velocity ( in cm/s) of image wrt a stationary observer in situation shown in the figure. Object and mirror move towards right with velocities of 10 cm/s and 2 cm/s respectively.

1. 1 cm/s
2. 2 cm/s
3. \N
4. Can't be calculated

Q. An object and a plane mirror are shown in figure. Mirror is moved with velocity V as shown. The velocity of image is :

1. $2Vsin\theta$
2. $2V$
3. $2Vcos\theta$
4. none of these

Q. Find the velocity of image of a moving particle $\text{O}$ in the situation as shown in the figure.

1. $\sqrt{104}\text{m/s}$, at ${\tan }^{-1}\left(\frac{1}{5}\right)$ with vertical.
2. $\sqrt{68}\text{m/s}$, at ${\tan }^{-1}\left(\frac{1}{2}\right)$ with vertical
3. $\sqrt{164}\text{m/s}$, at ${\tan }^{-1}\left(4/5\right)$ with horizontal
4. $10\text{m/s}$, at ${53}^{\circ }$ with horizontal

Q. I wrote an email to the manufacture of my bike's rear view mirror that the following warning should also be written on it: 'objects are faster than they appear' on my rear view mirror. Will this warning always be true?

1. Data insuffcient to comment
2. No
3. Yes

Q. A car is fitted with a convex side – view mirror of local length 20 cm. A second car 2.8 m behind the first car is overtaking the first car at a relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is:

1. 10 m/s
2. 15 m/s
3. $\frac{1}{10}m/s$
4. $\frac{1}{15}m/s$

Q. What is the velocity (in cm/s) of image in situation shown below? Object moves with velocity 10 cm/s and mirror moves with velocity 2 cm/s as shown.

1. 2 cm/s
2. 0 cm/s
3. 4 cm/s
4. 1 cm/s

Q. What is the velocity (in cm/s) of image in situation shown below? Object moves with velocity 10 cm/s and mirror moves with velocity 2 cm/s as shown.

1. 2 cm/s
2. 0 cm/s
3. 4 cm/s
4. 1 cm/s

Q. A car is fitted with a convex side – view mirror of local length 20 cm. A second car 2.8 m behind the first car is overtaking the first car at a relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is:

1. $\frac{1}{10}m/s$
2. $\frac{1}{15}m/s$
3. 10 m/s
4. 15 m/s

Q. I wrote an email to the manufacture of my bike's rear view mirror that the following warning should also be written on it: 'objects are faster than they appear' on my rear view mirror. Will this warning always be true?

1. No
2. Yes
3. Data insuffcient to comment

Q. A man of mass m starts moving w.r.t. a platform of mass 2m with a velocity $u=\frac{9}{13}m/s$ as shown in the figure. The platform is fitted with a concave mirror of focal length f. The velocity of image (in m/s) at the initial moment is :