Moving Object, Stationary Plane Mirror

Q. Three plane mirrors are kept as shown in the figure. A point object $O$ is kept at the centroid of the equilateral triangle. Which of the following statements is/are true.

1. Total number of images formed by three mirror system is $12$.
2. All the images formed by the plane mirrors $AB$ and $BC$ and object lie on the periphery of circle centred at $B$.
3. Number of images formed by any two mirrors in the given three mirror system is equal to $4$.
4. Number of images formed by any two mirrors in the given three mirror system is equal to $5$.

Q. Two plane mirrors of length $L$ are separated by distance $L$ and a man $M_2$ is standing at distance $L$ from the connecting line of mirrors as shown in figure. A man $M_1$ is walking in a straight line at distance $2L$ parallel to mirrors at speed $U$. The time for which man $M_2$ at O will be able to see image of $M_1$ is

1. $\frac{3L}{U}$
2. $\frac{8L}{U}$
3. $\frac{6L}{U}$
4. $\frac{nL}{U}$

Q. A man runs towards a mirror at a speed $+6\text{m/s}$. If the mirror is at rest, his image will have a velocity (with respect to man)

1. $12\text{m/s}$
2. $6\text{m/s}$
3. $-6\text{m/s}$
4. $-12\text{m/s}$

Q. An object is approaching a fixed plane mirror with velocity $10\text{m/s}$ making an angle of ${60}^{\circ }$ with the normal to the mirror. The speed of image with respect to the mirror is

1. $20\text{m/s}$
2. $25\text{m/s}$
3. $15\text{m/s}$
4. $10\text{m/s}$

Q. The width of man's face is $D$. The distance between the eyes of the man is $d$. Then the minimum width of plane mirror to see his full face is

1. $\frac{D-d}{4}$
2. $\frac{D-d}{2}$
3. $D-d$
4. $\frac{D+d}{2}$

Q. A plane mirror $50\text{cm}$ long hung on a vertical wall of a room with its lower edge $50\text{cm}$ above the ground. A man is standing in front of the mirror at $2\text{m}$ distance. If his eyes are $1.8\text{m}$ above the ground, then the length of the floor visible to him in the mirror is :

1. $\frac{45}{26}\text{m}$
2. $\frac{35}{13}\text{m}$
3. $100\text{cm}$
4. $90\text{cm}$

Q. A person $AB$ of height $170\text{cm}$ is standing in front of a plane mirror. His eyes are at height $164\text{cm}$. At what distance from $P$ should a hole be made in the mirror so that he cannot see his hairs?

1. $167\text{cm}$
2. $161\text{cm}$
3. $163\text{cm}$
4. $165\text{cm}$

Q. A plane mirror is placed along the $y$ - axis such that the $x$ - axis is normal to the plane of the mirror. The reflecting surface of the mirror is towards the negative $x$ - axis. The mirror moves in positive $x$ - direction with uniform speed of $5\text{m/s}$ and a point object $P$ is moving with constant speed of $3\text{m/s}$ in negative $x$ - direction. The speed of the image with respect to the mirror will be

1. $8\text{m/s}$
2. $2\text{m/s}$
3. $4\text{m/s}$
4. $6\text{m/s}$

Q. A fish F, in the pond is at a depth of $0.8m$ from the water surface and is moving vertically upward with velocity $2m{s}^{-1}$. At the same instant, a bird B is at a height of $6m$ from the water surface and is moving downward with velocity $3m{s}^{-1}$. At this instant, both are on the same vertical line as shown in the figure. Which of the following statement(s) are correct?

1. Height of B, observed by F (from itself), is equal to 5.30 m
2. Height of F, observed by B (from itself), is equal to 6.60 m
3. Height of B, observed by F (from itself), is equal to 8.80 m
4. None of the above

Q. An object moves with velocity $10\text{m/s}$ towards the left while the mirror moves with velocity $2\text{m/s}$ towards the right as shown in the figure. The velocity of image with respect to ground will be

1. $12\text{m/s}$ towards left
2. $12\text{m/s}$ towards right
3. $14\text{m/s}$ towards right
4. $14\text{m/s}$ towards left

Q. An object is appproaching a stationary plane mirror at $10\text{cm/s}$. A stationary observer sees the image. At what speed will the image approach the stationary observer?

1. $10\text{cm/s}$
2. $5\text{cm/s}$
3. $20\text{cm/s}$
4. $15\text{cm/s}$

Q. A particle is moving with velocity ($\hat{i}+2\hat{j}+3\hat{k})m/s$. A plane mirror exists in the x - y plane. The mirror has a velocity $(\hat{i}+2\hat{j})m/s$. Velocity of the image (in $m/s$) is:

1. $\hat{j}+\hat{k}$
2. $\hat{i}+2\hat{j}-3\hat{k}$
3. $-\hat{j}-\hat{k}$
4. None of these

Q. An elevator at rest which is at ${10}^{\text{th}}$ floor of a building is having a plane mirror fixed to its floor. A particle is projected with a speed, $v=\sqrt{2}{\text{ms}}^{-1}$ and at ${45}^{\circ }$ with the horizontal as shown in the figure. At the very instant of projection, the cable of the elevator breaks, and the elevator starts falling freely. What will be the separation between the particle and its image (in $\text{m}$), $0.5\text{s}$ after the instant of projection?

Q. The plane mirror shown in above figure is performing SHM with amplitude $A=3\text{cm}$. The amplitude of SHM of image wrt ground is

1. zero
2. $4\text{cm}$
3. $6\text{cm}$
4. $1.5\text{cm}$

Q. A ball is projected from top of a table with initial velocity $u$ at an angle $\theta$ with the horizontal as shown in the figure. The motion of image of ball with respect to the ball will be
$($Consider the plane mirror of sufficient height$)$

1. straight line along vertical direction
2. straight line along horizontal direction
3. a projectile
4. straight line or projectile depends on angle $\theta$

Q. A point object is moving with speed $v$ in front of the arrangement of two perpendicular plane mirrors as shown in the figure. The magnitude of velocity of image in mirror $M_1$ with respect to image in mirror $M_2$ will be

1. $2v$
2. $3v$
3. $0$
4. $v/2$

Q. A plane mirror is placed along the vertical plane (yz-plane). If a particle is also projected in the vertical plane with speed of projection $10\text{m/s}$ and angle of projection as ${60}^{\circ }$ from the normal direction to mirror. The point of projection is at a distance of $5\text{m}$ from the mirror, and the particle is directed towards the mirror. The magnitude of velocity of approach of particle and image, just before the particle touches the mirror is

1. $10\text{m/s}$
2. $10\sqrt{3}\text{m/s}$
3. $5\text{m/s}$
4. $5\sqrt{3}\text{m/s}$

Q. A point object $O$ and a mirror $M$ move with velocities of $3{\text{cm s}}^{-1}$ and $4{\text{cm s}}^{-1}$, respectively as shown in the figure. $O{O}^{\prime }$ is the normal to the mirror. The speed of the image will be -

1. $-7\hat{i}$
2. $7\hat{i}+2\sqrt{3}\hat{j}$
3. $-3\hat{i}+2\hat{j}$
4. $+7\hat{i}$

Q. An object $O$ is moving with velocity of $(\hat{i}+2\hat{j}+3\hat{k})\text{m/s}$ and a plane mirror in $yz$ plane facing the object is moving with velocity of $\left(2\hat{i}\right)\text{m/s}$. The velocity of the image with respect to ground (in SI units) will be

1. $2\hat{i}$
2. $-\hat{i}+2\hat{j}+3\hat{k}$
3. $3\hat{i}+2\hat{j}+3\hat{k}$
4. $2\hat{i}-3\hat{k}$

Q. A point object $O$ is moving with a velocity of $v$ in front of an arrangement of plane mirrors as shown in the figure. The magnitude of velocity of image in mirror $M_1$ with respect to the image in mirror $M_2$ will be

1. $3v\cos \theta$
2. $2v\cos \theta$
3. $3v\sin \theta$
4. $2v\sin \theta$

Q. A plane mirror is placed along the $y$ - axis such that the $x$ - axis is normal to the plane of the mirror. The reflecting surface of the mirror is towards the negative $x$ - axis. The mirror moves in positive $x$ - direction with uniform speed of $5\text{m/s}$ and a point object $P$ is moving with constant speed of $3\text{m/s}$ in negative $x$ - direction. The speed of the image with respect to the mirror will be

1. $8\text{m/s}$
2. $2\text{m/s}$
3. $4\text{m/s}$
4. $6\text{m/s}$

Q. A plane mirror is placed parallel to y-axis with its center at origin $(0,0,0)$. An object starts the motion in front of the mirror from position $(2,0)\text{m}$ with a velocity $(2\hat{i}+2\hat{j})\text{m/s}$. The relative velocity of image with respect to the object is along

1. positive x-axis
2. positive y-axis
3. negative y-axis
4. negative x-axis

Q. The origin of $x$ and $y$ coordinates is the pole of a concave mirror of focal length $20\text{cm}$. The $\text{x-axis}$ is the optical axis with $x>0$ being the rear side of mirror. A point object at the point $(30\text{cm},1\text{cm})$ is moving with a velocity $10\text{cm/s}$ in positive $\text{x-}$direction. The velocity of the image in $\text{cm/s}$ is approximately

1. $-80\hat{i}+8\hat{j}$
2. $-40\hat{i}-2\hat{j}$
3. $-40\hat{i}+2\hat{j}$
4. $40\hat{i}-4\hat{j}$

Q. An object is dropped from a height of $20\text{m}$. If a plane mirror is lying on the floor with the reflecting surface facing the object. The speed of image of the ball with respect to the ball just before striking the mirror will be
$($Take $g=10{\text{m/s}}^2)$

1. $40\text{m/s}$
2. $30\text{m/s}$
3. $10\text{m/s}$
4. $20\text{m/s}$

Q. An object is performing uniform circular motion in a horizontal $xy$ - plane in front of a plane mirror kept perpendicular to $xy$ - plane and reflecting surface facing the object. If the object is revolving in an anti-clockwise direction with speed $v$, then identify the correct statement regarding the motion of the image with respect to ground.

1. The image is moving on a straight line with speed $\frac{v}{\sqrt{2}}$
2. The image is revolving in clockwise direction with speed $2v$ on circular path
3. The image is revolving in anti-clockwise direction with speed $2v$ on circular path
4. The image is revolving in clockwise direction with speed $v$ on circular path

Q.
Two flat mirrors form an angle close to ${180}^{\circ }$ as shown in figure. A source of light S is placed at equal distances b from the mirrors. A screen is at distance a from mirrors. Wavelength of light is $\lambda$ and there is a shield C that block light passing directly to the screen, then

1. We get bright fringe t A
2. Fringe width at screen is $\frac{\lambda (a+b)}{4\alpha b}$
3. Fringe width increases as $\alpha$ increases
4. Fringe width at screen is $\frac{\lambda a\alpha }{2b}$

Q. A plane mirror is moving with velocity $(4\hat{i}+5\hat{j}+7\hat{k})\text{m/s}$. A point object in front of the mirror moves with a velocity $(3\hat{i}+4\hat{j}+5\hat{k})\text{m/s}$. Here $\hat{k}$ is along the normal to plane mirror and facing towards the object. The velocity of image w.r.t ground is (in SI units)

1. $3\hat{i}+4\hat{j}+9\hat{k}$
2. $-3\hat{i}-4\hat{j}+11\hat{k}$
3. $3\hat{i}-4\hat{j}+9\hat{k}$
4. $3\hat{i}+4\hat{j}+11\hat{k}$

Q. A cubical room is made by placing $6$ identical plane mirrors with the reflecting surface on the inside of the room. An insect crawls along the diagonal of the floor with constant speed of $40\text{cm/sec}$. What is the magnitude of velocity of image of insect w.r.t insect in one of the two adjacent walls?

1. $40\sqrt{2}\text{cm/s}$
2. $20\sqrt{2}\text{cm/s}$
3. $20\text{cm/s}$
4. $\frac{20}{\sqrt{2}}\text{cm/s}$

Q. Calculate the magnitude of velocity of the image $\left(V_s\right)$ with respect to a stationary observer in the following situation ( Object moving at an angle with the mirror and mirror is stationary).

1. $5\sqrt{2}m/s$
2. $5\sqrt{5}m/s$
3. $5\sqrt{10}m/s$
4. $5\sqrt{6}m/s$

Q. An object is moving towards a stationary plane mirror with a speed of $2m/s$ in left. Velocity of the image w.r.t. the object is

1. $2m/s$ towards right
2. $4m/s$ towards right
3. $2m/s$ towards left
4. $4m/s$ towards left