Moving Object, Stationary Plane Mirror

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. For the arrangement of mirror and object shown in figure, the velocity of image w.r.t ground is:

1. $-5\hat{i}+5\hat{j}\text{m/s}$
2. $-5(1+\sqrt{3})\hat{i}+5\hat{j}\text{m/s}$
3. $(-5-5\sqrt{3})\hat{i}+5\hat{j}\text{m/s}$
4. $-5(1+\sqrt{3})\hat{i}+5\sqrt{3}\text{m/s}$

Q. A ball at rest is projected horizontally from a table in front of a vertical plane mirror as shown in the figure. At any time $t$, the velocity of image with respect to ground can be written as :

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

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

Q. A bullet of mass $m_2$ is fired from a gun of mass $m_1$ with horizontal velocity $v$. A plane mirror is fixed to the gun facing towards the bullet. The velocity of the image of the bullet formed by the plane mirror with respect to the bullet is (Neglect the mass of mirror)

1. $(1+\frac{m_2}{m_1})v$
2. $\left(\frac{m_1+m_2}{m_1}\right)v$
3. $\frac{2(m_1+m_2)v}{m_1}$
4. $\frac{2(2m_1+m_2)v}{m_1}$

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

Q.

Paragraph for below question

नीचे दिये गये प्रश्न के लिए अनुच्छेद

An electron, a proton, an alpha particle and a neutron are projected in a external uniform magnetic field region with same linear momentum. The magnetic field is perpendicular and directed into the plane of the paper. The subsequent tracks of the particles are labelled in the figure.

एक बाह्य एकसमान चुम्बकीय क्षेत्र में एक इलेक्ट्रॉन, एक प्रोटॉन, एक अल्फा कण तथा एक न्यूट्रॉन को समान रेखीय संवेग से प्रक्षेपित किया जाता है। चुम्बकीय क्षेत्र कागज के तल के लम्बवत् अन्दर की ओर निर्देशित है। कणों के अनुवर्ती पथ चित्र में अंकित हैं।

Q. The order of track followed by electron, proton, alpha particle and neutron respectively will be

प्रश्न - इलेक्ट्रॉन, प्रोटॉन, अल्फा कण तथा न्यूट्रॉन द्वारा अनुसरित पथ का क्रम क्रमशः होगा

1. A, B, D, C
2. B, D, A, C
3. D, A, B, C
4. D, B, A, C

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

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

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. 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. 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. 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. A plane mirror is receding away from an observer at rest with a speed of $5\text{cm/s}$. If the observer can see his image in the mirror, then image recedes away with speed of

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

Q. This section contains 1 Matrix Match type question, which has 2 Columns (Column I and Column II). Column I has four entries (A), (B), (C) and (D), Column II has four entries (P), (Q), (R) and (S). Match the entries in Column I with the entries in Column II. Each entry in Column I may match with one or more entries in Column II.
इस खण्ड में 1 मैट्रिक्स मिलान प्रकार का प्रश्न है, जिसमें 2 कॉलम (कॉलम I तथा कॉलम II) हैं। कॉलम I में चार प्रविष्टियाँ (A), (B), (C) तथा (D) हैं, कॉलम II में चार प्रविष्टियाँ (P), (Q), (R) तथा (S) हैं। कॉलम I में दी गयी प्रविष्टियों का मिलान कॉलम II में दी गयी प्रविष्टियों के साथ कीजिए। कॉलम I में दी गयी प्रत्येक प्रविष्टि का मिलान कॉलम II में दी गयी एक या अधिक प्रविष्टियों के साथ हो सकता है।

A particle of charge q of mass m is projected inside a uniform magnetic field B, at an angle θ with the magnetic field with speed v. Different value of θ is given in Column-I and its effect is given in Column-II. Match the entries of Column-I with the entries of Column-II.

q आवेश व m द्रव्यमान के एक कण को एकसमान चुम्बकीय क्षेत्र B के अन्दर चुम्बकीय क्षेत्र से θ कोण पर चाल v से प्रक्षेपित किया जाता है। कॉलम-I में θ के भिन्न-भिन्न मान दिए गए हैं तथा कॉलम-II में इसके प्रभाव दिए गए हैं। कॉलम-I की प्रविष्टियों का मिलान कॉलम-II की प्रविष्टियों के साथ कीजिए।

	Column (कॉलम)-I		Column (कॉलम)-II
(A)	θ = 0°	(P)	Force acting on the particle is zero कण पर कार्यरत बल शून्य है
(B)	θ = 90°	(Q)	Force acting on the particle is qvB कण पर कार्यरत बल qvB है
(C)	θ = 180°	(R)	Path of the particle will be straight line कण का पथ सरल रेखीय होगा
(D)	θ = 60°	(S)	Path of the particle will be helix कण का पथ कुण्डलीनुमा होगा

1. A-PR, B-Q, C-PR, D-S
2. A-PQ, B-R, C-PR, D-S
3. A-PR, B-PS, C-PQ, D-R
4. A-PS, B-Q, C-R, D-P

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

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. According to a stationary observer on ground, a point object $O$ in front of a plane mirror $M$ and the mirror both are moving at $10\text{cm/s}$ and $20\text{cm/s}$ respectively towards right. Find the speed of the image as measured by the stationary observer.

1. $10\text{cm/s}$
2. $5\text{cm/s}$
3. $20\text{cm/s}$
4. $30\text{cm/s}$

Q. For an object moving with a speed $v$ in front of a plane mirror as shown in the figure, identify the correct diagram representing motion of its image with respect to ground.

1. 
2. 
3. 
4. 

Q. An object is moving with velocity $\frac{1}{2}(\hat{i}+\sqrt{3}\hat{j})\text{m/s}$ such that its image in the plane mirror is moving with velocity $\frac{1}{2}(\hat{i}-\sqrt{3}\hat{j})\text{m/s}$ where $\hat{i}$ and $\hat{j}$ are unit vectors along $+x$ and $+y$ - axis respectively. For the situation described above, identify the incorrect statement.

1. Mirror is moving along $y$ - axis.
2. Mirror might be stationary along $x$ - axis.
3. Normal of mirror is along $y$ - axis
4. Object is moving in $xy$ - plane.

Q. According to a stationary observer on ground, a point object $O$ in front of a plane mirror $M$ and the mirror both are moving at $10\text{cm/s}$ and $20\text{cm/s}$ respectively towards right. Find the speed of the image as measured by the stationary observer.

1. $10\text{cm/s}$
2. $5\text{cm/s}$
3. $20\text{cm/s}$
4. $30\text{cm/s}$

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

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

Q. A ball at rest is projected horizontally from a table in front of a vertical plane mirror as shown in the figure. At any time $t$, the velocity of image with respect to ground can be written as :

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

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 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. The plane mirror shown in the 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 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. $100\text{cm}$
2. $\frac{35}{13}\text{m}$
3. $90\text{cm}$
4. $\frac{45}{26}\text{m}$