A uniform metallic
Question: A uniform metallic wire is elongated by $0.04 \mathrm{~m}$ when subjected to a linear force $\mathrm{F}$. The elongation, if its length and diameter is doubled and subjected to the same force will be ___________ $\mathrm{cm}$. Solution: $\mathrm{F}=\mathrm{Y} . \mathrm{A} . \frac{\Delta \ell}{\ell}$ $\Delta \ell=\frac{\mathrm{F}}{\mathrm{Y} \cdot \mathrm{A} .} \ell$ $\Delta \ell=\frac{\mathrm{F} \ell}{\mathrm{Y} \cdot \pi \mathrm{r}^{2}}$ $\Delta \ell \propto \frac{\ell}{\mathrm{r}^{2}...
Read More →Thermodynamic process is shown below on
Question: Thermodynamic process is shown below on a $\mathrm{P}-\mathrm{V}$ diagram for one mole of an ideal gas. If $\mathrm{V}_{2}=2 \mathrm{~V}_{1}$ then the ratio of temperature $\mathrm{T}_{2} / \mathrm{T}_{1}$ is : $\frac{1}{2}$2$\sqrt{2}$$\frac{1}{\sqrt{2}}$Correct Option: , 3 Solution: $\mathrm{PV}^{1 / 2}=\mathrm{c}$ $\frac{\mathrm{nRT}}{\mathrm{V}} V^{1 / 2}=\mathrm{c}$ $T=c^{1} V^{1 / 2}$ $\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}=\left(\frac{\mathrm{V}_{2}}{\mathrm{~V}_{1}}\right)^{1 / ...
Read More →In a ferromagnetic material, below the curie temperature,
Question: In a ferromagnetic material, below the curie temperature, a domain is defined as :a macroscopic region with zero magnetization.a macroscopic region with consecutive magnetic dipoles oriented in opposite direction.a macroscopic region with randomly oriented magnetic dipoles.a macroscopic region with saturation magnetization.Correct Option: , 4 Solution: (4) conceptual...
Read More →A body weighs
Question: A body weighs $49 \mathrm{~N}$ on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator? (Use $\mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^{2}}=9.8 \mathrm{~ms}^{-2}$ and radius of earth, $\mathrm{R}=6400 \mathrm{~km} .]$$49 \mathrm{~N}$$48.83 \mathrm{~N}$$49.83 \mathrm{~N}$$49.17 \mathrm{~N}$Correct Option: , 2 Solution: Weight of pole $=\mathrm{mg}=49 \mathrm{~N}$ At equator due to rotation $=\mathrm{g}_{\mathr...
Read More →The mass per unit length of a uniform wire is
Question: The mass per unit length of a uniform wire is $0.135 \mathrm{~g} / \mathrm{cm}$. A transverse wave of the form $\mathrm{y}=-0.21 \sin (\mathrm{x}+30 \mathrm{t})$ is produced in it, where $x$ is in meter and $t$ is in second. Then, the expected value of tension in the wire is $x \times 10^{-2} \mathrm{~N}$. Value of $x$ is. (Round-off to the nearest integer) Solution: $\mu=0.135 \mathrm{gm} / \mathrm{cm}=0.0135 \mathrm{~kg} / \mathrm{m}$ $y=-0.21 \sin (x+30 t)$ $(x$ in meter \ $t$ in $s...
Read More →A particle is projected
Question: A particle is projected with velocity $v_{0}$ along $x$-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e., ma $=-\alpha x^{2} . .$ The distance at which the particle stops :$\left(\frac{3 v_{0}^{2}}{2 \alpha}\right)^{\frac{1}{2}}$$\left(\frac{2 v_{0}}{3 \alpha}\right)^{\frac{1}{3}}$$\left(\frac{2 v_{0}^{2}}{3 \alpha}\right)^{\frac{1}{2}}$$\left(\frac{3 v_{0}^{2}}{2 \alpha}\right)^{\frac{1}{3}}$Correct Option: , 4 So...
Read More →For extrinsic semiconductors;
Question: For extrinsic semiconductors; when doping level is increased;Fermi-level of p-type semiconductor will go upward and Fermi-level of n-type semiconductors will go downward.Fermi-level of p-type semiconductors will go downward and Fermi-level of n-type semiconductor will go upward.Fermi-level of both p-type and n-type semiconductros will go upward for $TT_{F}$ $K$ and downward for $TT_{F} K$, where $T_{F}$ is Fermi temperature.Fermi-level of $p$ and n-type semiconductors will not be affec...
Read More →A container is divided into two chambers by a partition.
Question: A container is divided into two chambers by a partition. The volume of first chamber is $4.5$ litre and second chamber is $5.5$ litre. The first chamber contain $3.0$ moles of gas at pressure $2.0$ atm and second chamber contain $4.0$ moles of gas at pressure $3.0$ atm. After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is $x \times 10^{-1}$ atm. Value of $x$ is. Solution: Let common equilibrium pressure of ...
Read More →Match List - I with List - II.
Question: Match List - I with List - II. Choose the correct answer from the options given below :$(\mathrm{a})-(\mathrm{vi}),(\mathrm{b})-(\mathrm{iv}),(\mathrm{c})-(\mathrm{i}),(\mathrm{d})-(\mathrm{v})$(a)-(vi), (b)-(v), (c)-(i), (d)-(iv)(a)-(ii), (b)-(iv), (c)-(vi), (d)-(iii)(a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)Correct Option: , 4 Solution: (a) Source of microwave frequency is magnetron. (b) Source of infrared frequency is vibration of atoms and molecules. (c) Source of Gamma rays is radioac...
Read More →Zener breakdown occurs
Question: Zener breakdown occurs in a $p-n$ junction having $\mathrm{p}$ and $\mathrm{n}$ both :lightly doped and have wide depletion layer.heavily doped and have narrow depletion layer.lightly doped and have narrow depletion laver.heavily doped and have wide depletion layer.Correct Option: , 2 Solution: Zener diode is heavily doped and have narrow depletion layer. Option (2) is correct....
Read More →As shown in the figure, a block of mass
Question: As shown in the figure, a block of mass $\sqrt{3} \mathrm{~kg}$ is kept on a horizontal rough surface of coefficient of friction $\frac{1}{3 \sqrt{3}}$. The critical force to be applied on the vertical surface as shown at an angle $60^{\circ}$ with horizontal such that it does not move, will be $3 \mathrm{x}$. The value of $\mathrm{x}$ will be $\left[\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2} ; \sin 60^{\circ}=\frac{\sqrt{3}}{2} ; \cos 60^{\circ}=\frac{1}{2}\right]$ Solution: $\mathrm{...
Read More →The potential energy (U) of a diatomic molecule
Question: The potential energy (U) of a diatomic molecule is a function dependent on $r$ (interatomic distance) as $\mathrm{U}=\frac{\alpha}{\mathrm{r}^{10}}-\frac{\beta}{\mathrm{r}^{5}}-3$ where, $\alpha$ and $\beta$ are positive constants. The equilibrium distance between two atoms will be $\left(\frac{2 \alpha}{\beta}\right)^{\frac{a}{b}}$, where $a=$_________. Solution: For equilibrium $\frac{\mathrm{dU}}{\mathrm{dr}}=0$ $\frac{-10 \alpha}{r^{11}}+\frac{5 \beta}{r^{6}}=0$ $\frac{5 \beta}{r^{...
Read More →A circular hole of radius
Question: A circular hole of radius $\left(\frac{a}{2}\right)$ is cut out of a circular disc of radius 'a' as shown in figure. The centroid of the remaining circular portion with respect to point ' $O^{\prime}$ will be : $\frac{1}{6} \mathrm{a}$$\frac{10}{11} \mathrm{a}$$\frac{5}{6} \mathrm{a}$$\frac{2}{3} a$Correct Option: , 3 Solution: Let $\sigma$ be the uniform mass density of disc then $\mathrm{x}_{\mathrm{COM}}=\frac{\left(\sigma \pi \mathrm{a}^{2}\right) \mathrm{a}-\sigma \pi\left(\frac{\...
Read More →A monoatomic gas of mass 4.0 u is kept in an insulated container.
Question: A monoatomic gas of mass $4.0 \mathrm{u}$ is kept in an insulated container. Container is moving with velocity $30 \mathrm{~m} / \mathrm{s}$. If container is suddenly stopped then change in temperature of the gas $(R=$ gas constant $)$ is $\frac{x}{3 R} .$ Value of $x$ is_______. Solution: Given that mass of gas is $4 u$ hence its molar mass $M$ is $4 \mathrm{~g} / \mathrm{mol}$ $\therefore \frac{1}{2} \mathrm{mv}^{2}=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}$ $\frac{1}{2} \mathrm{~m}...
Read More →A boy pushes a box of mass
Question: A boy pushes a box of mass $2 \mathrm{~kg}$ with a force $\overrightarrow{\mathrm{F}}=(20 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}) \mathrm{N}$ on a frictionless surface. If the box was initially at rest, then $\mathrm{m}$ is displacement along the x-axis after $10 \mathrm{~s}$. Solution: $\overrightarrow{\mathrm{F}}=20 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}$ $\overrightarrow{\mathrm{a}}=\frac{\overrightarrow{\mathrm{F}}}{\mathrm{m}}=\frac{20 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}}{2} \Rightar...
Read More →If the source of light
Question: If the source of light used in a Young's double slit experiment is changed from red to violet :consecutive fringe lines will come closer.the central bright fringe will become a dark fringe.the fringes will become brighter.the intensity of minima will increase.vCorrect Option: 1 Solution: $\beta=\frac{\lambda . D}{d}$ $\lambda_{\mathrm{R}}\lambda_{\mathrm{V}}$ $\beta_{\mathrm{R}}=\frac{\lambda_{\mathrm{R}} \mathrm{D}}{\mathrm{d}}$ and $\beta_{\mathrm{V}}=\frac{\lambda_{\mathrm{V}} \math...
Read More →A coil of inductance 2H having negligible resistance
Question: A coil of inductance $2 \mathrm{H}$ having negligible resistance is connected to a source of supply whose voltage is given by $\mathrm{V}=3 \mathrm{t}$ volt. (where $t$ is in second). If the voltage is applied when $\mathrm{t}=0$, then the energy stored in the coil after $4 \mathrm{~s}$ is________ $\mathrm{J}$. Solution: $\varepsilon=\frac{\mathrm{LdI}}{\mathrm{dt}}$ $3 \int_{0}^{4} \mathrm{t} d \mathrm{t}=2 \int_{0}^{1} \mathrm{dI}$ $\frac{3}{2} \times 16=2 I$ $\mathrm{I}=12$ $\mathrm...
Read More →A radiation is emitted by
Question: A radiation is emitted by $1000 \mathrm{~W}$ bulb and it generates an electric field and magnetic field at $\mathrm{P}$, placed at a distance of $2 \mathrm{~m}$. The efficiency of the bulb is $1.25 \%$. The value of peak electric field at $P$ is $x \times 10^{-1} \mathrm{~V} / \mathrm{m}$. Value of $x$ is_. (Rounded-off to the nearest integer) $\left[\right.$ Take $\varepsilon_{0}=8.85 \times 10^{-12} \mathrm{C}^{2} \mathrm{~N}^{-1} \mathrm{~m}^{-2}, \mathrm{c}=3 \times 10^{8}$ $\left....
Read More →512 identical drops of mercury are charged
Question: 512 identical drops of mercury are charged to a potential of $2 \mathrm{~V}$ each. The drops are joined to form a single drop. The potential of this drop is__________ $\mathrm{V}$. Solution: $Q=512 q$ Volume $_{\mathrm{i}}=$ Volume $_{\mathrm{f}}$ $512 \times \frac{4}{3} \pi r^{3}=\frac{4}{3} \pi R^{3}$ $2^{9} r^{3}=R^{3}$ $\mathrm{R}=8 \mathrm{r}$ $2=\frac{\mathrm{kq}}{\mathrm{r}}$ $\mathrm{V}=\frac{\mathrm{kQ}}{\mathrm{R}}=\frac{\mathrm{k} 512 \mathrm{q}}{8 \mathrm{r}}$ $\mathrm{V}=1...
Read More →512 identical drops of mercury are charged
Question: 512 identical drops of mercury are charged to a potential of $2 \mathrm{~V}$ each. The drops are joined to form a single drop. The potential of this drop is__________ $\mathrm{V}$. Solution: $Q=512 q$ Volume $_{\mathrm{i}}=$ Volume $_{\mathrm{f}}$ $512 \times \frac{4}{3} \pi r^{3}=\frac{4}{3} \pi R^{3}$ $2^{9} r^{3}=R^{3}$ $\mathrm{R}=8 \mathrm{r}$ $2=\frac{\mathrm{kq}}{\mathrm{r}}$ $\mathrm{V}=\frac{\mathrm{kQ}}{\mathrm{R}}=\frac{\mathrm{k} 512 \mathrm{q}}{8 \mathrm{r}}$ $\mathrm{V}=1...
Read More →The circuit contains two diodes each with a forward resistance
Question: The circuit contains two diodes each with a forward resistance of $50 \Omega$ and with infinite reverse resistance. If the battery voltage is $6 \mathrm{~V}$, the current through the $120 \Omega$ resistance is $\mathrm{mA}$. Solution: In this circuit $D_{1}$ will be forward bias and $D_{2}$ will be revers bias. $\therefore$ There will be no current through $\mathrm{D}_{2}$ and $\mathrm{R}_{2}$ Apply KVL in circuit we get $+6-50 \mathrm{i}-130 \mathrm{i}-120 \mathrm{i}=0$ $i=\frac{6}{30...
Read More →The same size images are formed by a convex lens
Question: The same size images are formed by a convex lens when the object is placed at $20 \mathrm{~cm}$ or at $10 \mathrm{~cm}$ from the lens. The focal length of convex lens is_________ $\mathrm{cm}$. Solution: $m=\frac{f}{u+f}$ $+m=\frac{f}{-10+f}$..........(1) $-m=\frac{f}{-20+f} \quad \cdots$(2) (1) / (2) $-1=\frac{f-20}{f-10}$ $10-f=f-20$ $30=2 f$ $f=15 \mathrm{~cm}$...
Read More →According to Bohr
Question: According to Bohr atom model, in which of the following transitions will the frequency be maximum ?$\mathrm{n}=4$ to $\mathrm{n}=3$$\mathrm{n}=2$ to $\mathrm{n}=1$$n=5$ to $n=4$$\mathrm{n}=3$ to $\mathrm{n}=2$Correct Option: , 2 Solution: $\Delta \mathrm{E}=13.6\left[\frac{1}{\mathrm{n}_{1}^{2}}-\frac{1}{\mathrm{n}_{2}^{2}}\right]=\mathrm{hv}$ It is maximum if $\mathrm{n}_{1}=1$ and $\mathrm{n}_{2}=2$ Option (2) is correct....
Read More →In an electrical circuit, a battery is connected to pass
Question: In an electrical circuit, a battery is connected to pass $20 \mathrm{C}$ of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at $15 \mathrm{~V}$. The work done by the battery is Solution: Work done by battery $=Q(\Delta V)$ $\Rightarrow 20 \times 15=300 \mathrm{~J}$ $\therefore$ Ans. 300...
Read More →Which of the following
Question: Which of the following equations represents a travelling wave ?$y=\operatorname{Asin}(15 x-2 t)$$\mathrm{y}=\mathrm{Ae}^{-x^{2}}(v t+\theta)$$\mathrm{y}=\operatorname{Ae}^{x} \cos (\omega t-\theta)$$y=A \sin x \cos \omega t$Correct Option: 1 Solution: $\mathrm{y}=\mathrm{F}(\mathrm{x}, \mathrm{t})$ For travelling wave $y$ should be linear function of $\mathrm{x}$ and $\mathrm{t}$ and they must exist as $(\mathrm{x} \pm \mathrm{vt})$ $\mathrm{y}=A \sin (15 x-2 t) \rightarrow$ linear fun...
Read More →