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MODEL PAPER 7 Physics - MODEL PAPER 7

CBSE - STD 12 Science - Physics (CBSE - English Medium). 38 questions in this chapter.

Question types

MODEL PAPER 7 question types

38 questions across 6 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.

38
Questions
6
Question groups
5
Question types
Sample Questions

MODEL PAPER 7 questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
A microscope is focused on a mark. Then a glass slab of refractive index 1.5 and thickness 6 cm is placed on the mark. To get the mark again in focus the microscope should be moved
  • A
    9 cm upward c) 4 cm upward
  • B
    2 cm downward
  • C
    4 cm upward
  • D
    2 cm upward
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Q 3M.C.Q (1 Marks)1 Mark
An electric dipole placed in a non-uniform electric field can experience
  • A
    always a force and a torque.
  • B
    neither a force nor a torque.
  • C
    a force but not a torque.
  • D
    a torque but not a force.
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Q 4M.C.Q (1 Marks)1 Mark
In Huygens' theory, light waves
  • A
    are transverse waves and require no medium to travel.
  • B
    are longitudinal waves and require a medium to travel.
  • C
    are transverse waves and require a medium to travel.
  • D
    are longitudinal waves and require no medium to travel.
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Q 5M.C.Q (1 Marks)1 Mark
Consider the two idealised systems: (i) a parallel plate capacitor with large plates and small separation and (ii) a long solenoid of length L > > R, radius of cross-section. In (i), E is ideally treated as a constant between plates and zero outside. In (ii), magnetic field is constant inside the solenoid and zero outside. These idealised assumptions, however, contradict fundamental laws as below:
  • A
    case (ii) contradicts Gauss's law for magnetic fields.
  • B
    case (i) contradicts Gauss's law for electrostatic fields.
  • C
    case (ii) contradicts en $\oint H \cdot d 1=I_{e n}$
  • D
    case (i) agrees with $\oint E . d 1=0$
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Q 6Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A): If the frequency of the applied AC is doubled, then the power factor of a series R-L circuit decreases.
Reason (R): Power factor of series R-L circuit is given by \$\cos \phi=\frac{2 R}{R^2+\omega^2 L^2}$
  • A
    Both A and R are true and R is the correct explanation of A.
  • B
    Both A and R are true but R is not the correct explanation of A.
  • C
    A is true but R is false.
  • D
    A is false but R is true.
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Q 7Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A): To observe diffraction of light, the size of the obstacle/aperture should be of the order of $10^{-7} m$.
Reason (R): $10^{-7}$ is the order of the wavelength of visible light.
  • A
    Both A and R are true and R is the correct explanation of A.
  • B
    Both A and R are true but R is not the correct explanation of A.
  • C
    A is true but R is false.
  • D
    A is false but R is true.
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Q 8Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A): Two adjacent conductors of unequal dimensions, carrying the same positive charge have a potential difference between them.
Reason (R): The potential of a conductor depends upon the charge given to it.
  • A
    Both A and R are true and R is the correct explanation of A.
  • B
    Both A and R are true but R is not the correct explanation of A.
  • C
    A is true but R is false.
  • D
    A is false but R is true.
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Q 9Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A): In the process of photoelectric emission, all emitted electrons have the same kinetic energy.
Reason (R): According to Einstein's equation $E_k=h v-\phi_0$.
  • A
    Both A and R are true and R is the correct explanation of A.
  • B
    Both A and R are true but R is not the correct explanation of A.
  • C
    A is true but R is false.
  • D
    A is false but R is true.
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Q 102 Marks Questions2 Marks
Which one of the following will describe the smallest circle when projected with the same velocity $v$ perpendicular to the magnetic field $B: (i)\ \alpha-$particle, and $(ii)\ \beta-$particle?
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Q 112 Marks Questions2 Marks
A proton and an alpha particle having the same kinetic energy are, in turn, passed through a region of the uniform magnetic field, acting normal to the plane of the paper and travel in circular paths. Deduce the ratio of the radii of the circular paths described by them.
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Q 122 Marks Questions2 Marks
An $\alpha$-particle moving with initial kinetic energy $K$ towards a nucleus of atomic number $Z$ approaches a distance $d$ at which it reverses its direction. Obtain the expression for the distance of closest approach $d$ in terms of the kinetic energy of $\alpha$-particle $K$.
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Q 132 Marks Questions2 Marks
Determine the number density of donor atoms which have to be added to an intrinsic germanium semiconductor to produce an n-type semiconductor of conductivity $5 \Omega^{-1} cm^{-1}$, given that the mobility of electron in $n-$type Ge is $3900 cm^2 /$ vs. Neglect the contribution of holes to conductivity.
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Q 153 Marks Question3 Marks
Define the term self$-$inductance of a solenoid. Obtain the expression for the magnetic energy stored in an inductor of self$-$inductance $L$ to build up a current $I$ through it.
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Q 163 Marks Question3 Marks
Figure shows a rectangular conducting loop $\text{PQRS}$ in which arm $RS$ of length $I$ is movable. The loop is kept in a uniform magnetic field $B$ directed downward perpendicular to the plane of the loop. The arm $RS$ is moved with a uniform speed $v$.
Image

Deduce an expression for
$i$. the emf induced across the arm $RS$
$ii$. the external force required to move the arm and
$iii$. the power dissipated as heat.
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Q 173 Marks Question3 Marks
Define the term wavefront. State Huygen's principle. Consider a plane wavefront incident on a thin convex lens. Draw a proper diagram to show how the incident wavefront traverses through the lens and after refraction focusses on the focal point of the lens, giving the shape of the emergent wavefront.
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Q 183 Marks Question3 Marks
$a.$ Using the Bohr's model, calculate the speed of the electron in a hydrogen atom in the $n = 1, 2$ and $3$ levels.
$b.$ Calculate the orbital period in each of these levels.
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Q 193 Marks Question3 Marks
We are given the following atomic masses:
${ }_{92}^{238} U=238.05079 u$
${ }_2^4 H e=4.00260 u$
${ }_{90}^{234} Th =234.04363 u$
${ }_1^1 H=1.00783 u$
${ }_{91}^{237} Pa=237.05121 u $
Here the symbol Pa is for the element protactinium $(Z = 91).$
$i.$ Calculate the energy released during the alpha decay of ${ }_{92}^{238} U$.
$ii.$ Calculate the kinetic energy of the emitted $\alpha$-particles.
$iii.$ Show that ${ }_{92}^{238} U$ can not spontaneously emit a proton.
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Q 205 Marks Questions5 Marks
i. With the help of a diagram, explain the principle and working of a device which produces current that reverses its direction after regular intervals of time.
ii. If a charged capacitor C is short-circuited through an inductor L, the charge and current in the circuit oscillate simple harmonically. a. In what form the capacitor and the inductor store energy? b. Write two reasons due to which the oscillations become damped.
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Q 215 Marks Questions5 Marks
$a$. Draw the diagram of a device which is used to decrease high $ac$ voltage into a low $ac$ voltage and state its working principle. Write four sources of energy loss in this device.
$b$. A small town with a demand of $1200 kW$ of electric power at $220 V$ is situated $20 \ km$ away from an electric plant generating power at $440 V$ . The resistance of the two wire line carrying power is $0.5 \Omega \ \text{per} \ \ km$. The town gets the power from the line through a $4000-220 V$ step $-$ down transformer at a sub $-$ station in the town. Estimate the line power loss in the form of heat
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Q 225 Marks Questions5 Marks
Two point charges $q$ and $-q$ are located at points $(0,0,-a)$ and $(0,0, a)$ respectively.
$i$. Find the electrostatic potential at $(0,0, z)$ and $(x, y, 0)$.
$ii.$ How much work is done in moving a small test charge from the point $(5,0,0)$ to $(-7,0,0)$ along the $X$-axis?
$iii.$ How would your answer change if the path of the test charge between the same points is not along the $x$-axis but along any other random path?
$iv$. If the above point charges are now placed in the same positions in a uniform external electric field $\vec{E}$, what would be the potential energy of the charge system in its orientation of unstable equilibrium? Justify your answer in each case.
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Q 235 Marks Questions5 Marks
Derive an expression for potential due to a dipole for distances large compared to the size of the dipole. How is the potential due to dipole different from that due to a single charge?
Image
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Q 245 Marks Questions5 Marks
Figure shows an outline of Lloyd's mirror experiment. $M$ is a plane mirror; $S$ is a narrow slit illuminated by some source of light $($not shown$)$ and $S$' is the image of S in $M. M, S$ and $S$' are in a plane perpendicular to the paper. $O$ is the line of intersection of the mirror and the screen.
$a.$ What is the origin of fringes observed on the screen? 
Image

$b$. Why is the slit S placed so as to have very oblique angle of incidence of light striking the mirror?
$c.$ The two path lengths $PS$ and $PS$' are equal when $P$ coincides with $O$. Yet the fringe at $O$ is found in the experiment to be dark not bright. What does this observation imply?
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Q 25Case study (4 Marks)4 Marks
Net electric flux through a cube is the sum of fluxes through its six faces. Consider a cube as shown in figure, having sides of length $L =10.0 \ cm$. The electric field is uniform, has a magnitude $E =4.00 \times 10^3 NC ^{-1}$ and is parallel to the $xy$ plane at an angle of $37^{\circ}$ measured from the $+ x -$axis towards the $+ y -$axis.
Image
$(i)$ Electric flux passing through surface $S_6$ is
$(a) \ -24 \ Nm ^2 C ^{-1}$
$(b) \ 32 \ Nm ^2 C ^{-1}$
$(c) \ -32 \ Nm ^2 C ^{-1}$
$(d)\  24 \ Nm ^2 C ^{-1}$
$(ii)$ Electric flux passing through surface $S_1$ is
$(a)-32 \ Nm ^2 C ^{-1}$
$(b) -24 \ Nm ^2 C ^{-1}$
$(c)\ 32 \ Nm ^2 C ^{-1}$
$(d)\ 24 \ Nm ^2 C ^{-1}$
$(iii)$ The surfaces that have zero flux are
$(a) S _2$ and $S _4  \ (b)  S_3$ and $S_6  \ (c)  S _1$ and $S _2  \ (d)  S _1$ and $S _3$
$(iv)$ he total net electric flux through all faces of the cube is $a) 24 \ Nm^2 C-1 c)-8 \ Nm^2 C-1$
$(a) \ 24 \ Nm ^2 C ^{-1}  \ (b) \  8 \ Nm ^2 C ^{-1}  \ (c)  \ -8 \ Nm ^2 C ^{-1}  \ (d)$ zero
OR
The dimensional formula of surface integral $\oint \vec{E} \cdot d \vec{S}$ of an electric field is
$(a) \ \left[ M ^{-1} L^3 T^{-3} A\right]$
$(b)\  \left[ M L ^2 T^{-2} A^{-1}\right]$
$(c) \ \left[ ML ^3 T^{-3} A^{-1}\right]$
$(d) \ \left[ M L ^{-3} T^{-3} A^{-1}\right]$
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Q 26Case study (4 Marks)4 Marks
A stationary charge produces only an electrostatic field while a charge in uniform motion produces a magnetic field, that does not change with time. An oscillating charge is an example of accelerating charge. It produces an oscillating magnetic field, which in turn produces an oscillating electric fields and so on. The oscillating electric and magnetic fields regenerate each other as a wave which propagates through space.
Image
$(i).$ Magnetic field in a plane electromagnetic wave is given by $\vec{B}= B _0 \sin ( kx +\omega t ) \hat{j} T$Expression for corresponding electric field will be (Where c is speed of light.)
$(a) \vec{E}= B _0 c \sin ( kx +\omega t ) \hat{k} V / m$
$(b) \vec{E}=- B _0 c \sin ( kx -\omega t ) \hat{k} V / m$
$(c) \vec{E}=- B _0 c \sin ( kx +\omega t ) \hat{k} V / m$
$(d) \vec{E}=\frac{B_0}{c} \sin ( kx +\omega t ) \hat{k} V / m$
$(ii)$ The electric field component of a monochromatic radiation is given by $\vec{E}=2 E _0 \hat{i} \cos kz \cos \omega t$. Its magnetic field $\vec{B}$ is then given by
$(a) -\frac{2 E_0}{c} \hat{j} \sin kz \sin \omega t$
$(b) \frac{2 E_0}{c} \hat{j} \sin kz \sin \omega t$
$(c) \frac{2 E_0}{c} \hat{j} \sin kz \cos \omega t$
$(d) \frac{2 E_0}{c} \hat{j} \cos kz \cos \omega t$
$(iii)$ A plane em wave of frequency $25 \ MHz$ travels in a free space along $x -$direction. At a particular point in space and time, $E =(6.3 \hat{j}) V / m$. What is magnetic field at that time?
$(a) \ 0.089 \mu T$
$(b) \ 0.124 \mu T$
$(c) \ 0.021 \mu T$
$(d) \ 0.095 \mu T$
OR
A plane electromagnetic wave travels in free space along $x-$axis. At a particular point in space, the electric field along $y$-axis is $9.3 V m ^{-1}$. The magnetic induction $(B)$ along $z -$axis is
$(a) \ 3.1 \times 10^{-8} T$
$(b) \ 3 \times 10^{-5} T$
$(c) \ 3 \times 10^{-6} T$
$(d) \ 9.3 \times 10^{-6} T$
$(iv)$ A plane electromagnetic wave travelling along the $x-$direction has a wavelength of $3 \ mm$ . The variation in the electric field occurs in the $y-$direction with an amptitude $66 V m ^{-1}$. The equations for the electric and magnetic fields as a function of $x$ and $t$ are respectively
$ \text { a) } E_y =11 \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right), \text { b) } E_y =66 \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right),$
$B_y =11 \times 10^{-7} \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right) B_z =2.2 \times 10^{-7} \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right)$
$\text { c) } E_x =33 \cos \pi \times 10^{11}\left(t-\frac{x}{c}\right), \text { d) } E_y =33 \cos \pi \times 10^{11}\left(t-\frac{x}{c}\right),$
$B_x =11 \times 10^{-7} \cos \pi \times 10^{11}\left(t-\frac{x}{c}\right) B_z =1.1 \times 10^{-7} \cos \pi \times 10^{11}\left(t-\frac{x}{c}\right)$
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