Moving Objects

Q. When an object is kept at a distance of $30\text{cm}$ from a concave mirror, the image is formed at a distance of $10\text{cm}$. If the object is moved with a speed of $9{\text{cms}}^{-1}$ in horizontal direction, the speed with which the image moves is

1. $0.1\text{cm/s}$
2. $1\text{cm/s}$
3. $3\text{cm/s}$
4. $9\text{cm/s}$

Q. A particle (object) is moving towards a fixed convex mirror. The image also moves. If $V_i=$ speed of image and $V_0=$ speed of the object, then

1. $V_i<V_0$ if $|u|<|F|$
2. $V_i>V_0$ if $|u|>|F|$
3. $V_i<V_0$ if $|u|>|F|$
4. $V_i=V_0$ if $|u|=|F|$

Q. A point object is moving along the principal axis of a concave mirror with uniform velocity towards the pole. Initially, the object is at an infinite distance from the pole on the right side of the mirror as shown. Before the object collides with the mirror, the number of times for which the distance between the object and its image is $50\text{cm}$ are

1. One time
2. Two times
3. Three times
4. More than three times

Q. A particle revolves in clockwise direction (as seen from point A) in a circle C of radius $1\text{cm}$ and completes one revolution in $2s$. The axis of the circle and the principal axis of the mirror $M$ coincide. The radius of curvature of the mirror is $20\text{cm}$. Then, the direction of revolution (as seen from A) of the image of the particle and its speed is

1. Clockwise, $3.14\text{cm/s}$
2. Anticlockwise, $1.57\text{cm/s}$
3. Anticlockwise, $3.14\text{cm/s}$
4. Clockwise, $1.57\text{cm/s}$

Q. The figure shows an object $O$ and its image $I$ formed by a mirror at $B$. If $AB$ is the principal axis of the mirror, the mirror is

1. plane
2. concave
3. either concave or convex
4. convex

Q. Find the velocity of images formed due to a point object $O$ w.r.t. ground if the mirror is at rest. All speeds given are w.r.t a stationary ground observer

1. $25\text{m/s}\text{towards mirror}$
2. $45\text{m/s}\text{towards mirror}$
3. $25\text{m/s}\text{away from mirror}$
4. $45\text{m/s}\text{away from mirror}$

Q. When an object is kept at a distance of $30\text{cm}$ from a concave mirror, the image is formed at a distance of $10\text{cm}$ from the mirror. If the object is moved with a speed of $9cm{s}^{-1}$, the speed (in $cm{s}^{-1}$) with which the image moves at that instant is .

Q. A concave spherical surface of radius of curvature $10cm$ separates two medium $x$ & $y$ of refractive index $4/3$ & $3/2$ respectively. If the object is placed along principal axis in medium $X$ then :

1. image is always real
2. image is real if the object distance is greater than 90 cm
3. image is always virtual
4. image is virtual if the object distance is less than 90 cm

Q. A particle revolves in clockwise direction (as seen from point A) in a circle C of radius $1\text{cm}$ and completes one revolution in $2\text{sec}$. The axis of the circle and the principal axis of the mirror M coincide, call it AB. The radius of curvature of the mirror is $20\text{cm}$. Then, the direction of revolution (as seen from A) of the image of the particle and its speed is

1. clockwise, $1.57{\text{cms}}^{-1}$
2. clockwise, $3.14{\text{cms}}^{-1}$
3. anticlockwise, $1.57{\text{cms}}^{-1}$
4. anticlockwise, $3.14{\text{cms}}^{-1}$

Q. A teacher held a pencil close to a spherical mirror and asked four students $W$, $X$, $Y$ and $Z$ to predict the nature of the mirror with the help of the image formed in the mirror. The image was erect and enlarged. The four students identified it as follows :
$W$ - Convex in nature
$X$ - Concave in nature
$Y$ - Plane mirror
$Z$ - Plano-concave mirror
The correct statement was given by _______

1. $Z$
2. $X$
3. $Y$
4. $W$

Q. A boy runs towards a convex mirror with a speed v. His image is seen to move towards the mirror at a speed $v^1$. Then,

1. $v>v^1$
2. $v<v^1$
3. $v=v^1$
4. Nothing can be said as data are insufficient,

Q. A certain mirror placed at the origin has $\hat{j}$ as the normal vector to its reflecting surface. The mirror begins to translate with a velocity $\hat{i}+\hat{j}+\hat{k}$ at $t=0$. At the same time an object which was initially at $\hat{i}+\hat{j}$ starts moving with a velocity $(\hat{i}+\hat{j})m/s$ , then which of the following is/are correct ?

1. initial position of the image will be $\hat{i}-\hat{j}$
2. The velocity of the image will be $\hat{i}+\hat{j}+2\hat{k}$
3. The velocity of image relative to the mirror will be $\hat{k}$
4. The velocity of image relative to the object will be $2\hat{k}$

Q. The velocity of the image with respect to ground in the below shown figure will be
$[$Mirror is at rest and velocity of the object $\left(O\right)$ perpendicular to the principal axis is given with respect to ground$]$

1. $10\text{m/s}$ moving downwards
2. $20\text{m/s}$ moving downwards
3. $20\text{m/s}$ moving upwards
4. $10\text{m/s}$ moving upwards

Q. The velocity of the image with respect to ground in the figure shown below figure will be :
$[$Mirror is at rest and velocity of the object $\left(O\right)$ is given with respect to ground$]$

1. $45\text{m/s}$ towards the mirror
2. $35\text{m/s}$ towards the mirror
3. $45\text{m/s}$ away from the mirror
4. $35\text{m/s}$ away from the mirror

Q. Find the velocity of images formed due to a point object $O$ w.r.t. ground if the mirror is at rest. All speeds given are w.r.t a stationary ground observer

1. $25\text{m/s}\text{towards mirror}$
2. $45\text{m/s}\text{towards mirror}$
3. $25\text{m/s}\text{away from mirror}$
4. $45\text{m/s}\text{away from mirror}$

Q. A particle revolves in clockwise direction (as seen from point $A$) in a circle $C$ of radius $1cm$ and completes one revolution in $2\sec$. The axis of the circle and the principal axis of the mirror $M$ coincide, a call it $AB$. The radius of curvature of the mirror is $20cm$. Then, the direction of revolution (as seen from $A$) of the image of the particle and its speed is

1. Clockwise, $1.57c{m}^{-1}$
2. Anticlockwise, $3.14c{m}^{-1}$
3. Clockwise, $3.14c{m}^{-1}$
4. Anticlockwise, $1.57c{m}^{-1}$

Q. A boy runs towards a convex mirror with a speed v. His image is seen to move towards the mirror at a speed v'. Then :

1. $v$
2. $v>v^{\prime }$
3. $v=v$
4. Nothing can be said as data are insufficient