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Question: Three students $S_{1}, S_{2}$ and $S_{3}$ perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table. (Least count of length $=0.1 \mathrm{~m}$ least count for time $=0.1 \mathrm{~s}$ ) If $\mathrm{E}_{1}, \mathrm{E}_{2}$ and $\mathrm{E}_{3}$ are the percentage errors in ' $\mathrm{g}$ ' for students 1,2 and 3 re...
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Question: The area of cross-section of a railway track is $0.01 \mathrm{~m}^{2}$. The temperature variation is $10^{\circ} \mathrm{C}$. Coefficient of linear expansion of material of track is $10^{-5} /{ }^{\circ} \mathrm{C}$. The energy stored per meter in the track is $\mathrm{J} / \mathrm{m}$. (Young's modulus of material of track is $10^{11} \mathrm{Nm}^{-2}$ ) Solution: Elastic energy $=\frac{\mathrm{Y}}{2}(\text { strain })^{2} \times$ Area $\times$ length $\Rightarrow \quad$ Elastic energ...
Read More →A ray of light passing through a prism
Question: A ray of light passing through a prism $(\mu=\sqrt{3})$ suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is (in degrees) Solution: At minimum deviation $r_{1}=r_{2}=\frac{A}{2}$ Also given $\mathrm{i}=2 \mathrm{r}_{1}=\mathrm{A}$ Now $1 \cdot \sin \mathrm{i}=\sqrt{3} \sin \mathrm{r}_{1}$ $1 \sin A=\sqrt{3} \sin \frac{A}{2}$ $\Rightarrow \quad 2 \sin \frac{A}{2} \cos \frac{A}{2}=\sqrt{3} \sin ...
Read More →A carrier wave
Question: A carrier wave $\mathrm{V}_{\mathrm{C}}(\mathrm{t})=160 \sin \left(2 \pi \times 10^{6} \mathrm{t}\right)$ volts is made to vary between $\mathrm{V}_{\max }=200 \mathrm{~V}$ and $\mathrm{V}_{\min }=120 \mathrm{~V}$ by a message signal $\mathrm{V}_{\mathrm{m}}(\mathrm{t})=\mathrm{A}_{\mathrm{m}} \sin \left(2 \pi \times 10^{3} \mathrm{t}\right)$ volts. The peak voltage $A_{m}$ of the modulating signal is_______. Solution: Maximum amplitude $A_{\max }=A_{m}+A_{C}$ $\Rightarrow V_{\max }=V_...
Read More →The centre of a wheel rolling on a plane surface moves with a speed
Question: The centre of a wheel rolling on a plane surface moves with a speed $v_{0}$. A particle on the rim of the wheel at the same level as the centre will be moving at a speed $\sqrt{\mathrm{x}} v_{0}$. Then the value of $\mathrm{x}$ is Solution: For no slipping $\mathrm{v}_{0}=\omega \mathrm{R}$ $\operatorname{Now} \mathrm{v}_{\mathrm{A}}=\mathrm{v}_{\mathrm{B}}=\sqrt{\mathrm{v}_{0}^{2}+(\omega \mathrm{R})^{2}}$ $=\sqrt{2} \mathrm{v}_{0}$ $\Rightarrow \quad x=2$...
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Question: If $\mathrm{q}_{\mathrm{f}}$ is the free charge on the capacitor plates and $\mathrm{q}_{\mathrm{b}}$ is the bound charge on the dielectric slab of dielectric constant $k$ placed between the capacitor plates, then bound charge $\mathrm{q}_{\mathrm{b}}$ can be expressed as :$\mathrm{q}_{\mathrm{b}}=\mathrm{q}_{\mathrm{f}}\left(1-\frac{1}{\sqrt{\mathrm{k}}}\right)$$\mathrm{q}_{\mathrm{b}}=\mathrm{q}_{\mathrm{f}}\left(1-\frac{1}{\mathrm{k}}\right)$$\mathrm{q}_{\mathrm{b}}=\mathrm{q}_{\mat...
Read More →The frequency of a car horn encountered
Question: The frequency of a car horn encountered a change from $400 \mathrm{~Hz}$ to $500 \mathrm{~Hz}$. When the car approaches a vertical wall. If the speed of sound is $330 \mathrm{~m} / \mathrm{s}$. Then the speed of car is_________ $\mathrm{km} / \mathrm{h}$. Solution: Wall as an observer Frequency received by wall $\mathrm{f}_{1}=\mathrm{f}_{0}\left(\frac{\mathrm{C}}{\mathrm{C}-\mathrm{V}}\right)$ Again wall as a source Frequency received by observer on car $f_{2}=f_{1}\left(\frac{C+V}{C}...
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Question: Three particles $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ are moving along the vectors $\overrightarrow{\mathrm{A}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}, \overrightarrow{\mathrm{B}}=\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{C}}=-\hat{\mathrm{i}}+\hat{\mathrm{j}}$ respectively. They strike on a point and start to move in different directions. Now particle $P$ is moving normal to the plane which contains vector $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm...
Read More →A balloon was moving upwards
Question: A balloon was moving upwards with a uniform velocity of $10 \mathrm{~m} / \mathrm{s}$. An object of finite mass is dropped from the balloon when it was at a height of $75 \mathrm{~m}$ from the ground level. The height of the balloon from the ground when object strikes the ground was around : (takes the value of $g$ as $10 \mathrm{~m} / \mathrm{s}^{2}$ )$300 \mathrm{~m}$$200 \mathrm{~m}$$125 \mathrm{~m}$$250 \mathrm{~m}$Correct Option: , 3 Solution: Object is projected as shown so as pe...
Read More →A body takes 4 min. to cool from 61° C to 59°C. If the temperature of the surroundings is 30°C,
Question: A body takes 4 min. to cool from 61 C to 59C. If the temperature of the surroundings is 30C, the time taken by the body to cool from 51C to 49 C is :4 min.3 min.8 min.6 min.Correct Option: , 4 Solution: $\frac{61-59}{4}=\mathrm{K}\left(\frac{61+59}{2}-30\right)$ .......(1) $\frac{51-49}{t}=K\left(\frac{51+49}{2}-30\right)$ ......(2) Divide (1) (2) $\frac{t}{4}=\frac{60-30}{50-30}=\frac{30}{20}$ so, $\mathrm{t}=6$ minutes...
Read More →An object viewed from a near point distance of
Question: An object viewed from a near point distance of $25 \mathrm{~cm}$, using a microscopic lens with magnification ' 6 ', gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length $0.6 \mathrm{~m}$, if the focal length of the eyepiece is equal to__________ $\mathrm{cm}$. Solution: For simple microscope, $\mathrm{m}=1+\frac{\mathrm{D}}{\mathrm{f}_{0}}$ $6=1+\frac{...
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Question: The total charge enclosed in an incremental volume of $2 \times 10^{-9} \mathrm{~m}^{3}$ located at the origin is $\mathrm{nC}$, if electric flux density of its field is found as $D=e^{-x} \sin y \hat{i}-e^{-x} \cos y \hat{j}+2 z \hat{k} \quad C / m^{2}$. Solution: Electric flux density $(\overrightarrow{\mathrm{D}})=\frac{\text { charge }}{\text { Area }} \times \hat{\mathrm{r}}=\frac{\mathrm{Q}}{4 \pi \mathrm{r}^{2}} \hat{\mathrm{r}}=\epsilon_{0}\left(\frac{\mathrm{Q}}{4 \pi \epsilon...
Read More →A rod of mass M and length L is lying on a horizontal
Question: A rod of mass $M$ and length $L$ is lying on a horizontal frictionless surface. A particle of mass ' $m$ ' travelling along the surface hits at one end of the rod with a velocity ' $u$ ' in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses $\left(\frac{\mathrm{m}}{\mathrm{M}}\right)$ is $\frac{1}{\mathrm{x}}$. The value of ' $x$ ' will be_______. Solution: Just before collision Just after collision Fr...
Read More →In an electric circuit, a call of certain emf provides
Question: In an electric circuit, a call of certain emf provides a potential difference of $1.25 \mathrm{~V}$ across a load resistance of $5 \Omega$. However, it provides a potential difference of $1 \mathrm{~V}$ across a load resistance of $2 \Omega$. The emf of the cell is given by $\frac{x}{10} \mathrm{~V}$. Then the value of $x$ is__________ Solution: Terminal voltage $v=i R=\frac{E R}{R+r}$ $1^{\mathrm{st}} \rightarrow 1.25=\frac{E(5)}{5+r}$ .......(I) $2^{\text {nd }} \rightarrow 1=\frac{E...
Read More →Assertion A : If in five complete rotations of the circular scale,
Question: Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 total divisions on circular scale, then least count is 0.001 cm. Reason R : Least Count $=\frac{\text { Pitch }}{\text { Totaldivisionson circular scale }}$ In the light of the above statements, choose the most appropriate answer from the options given below :A is not correct but R is correct.Both A and R are correct and R is the correct ex...
Read More →A circular disc reaches from top to bottom of an inclined
Question: A circular disc reaches from top to bottom of an inclined plane of length ' $L$ '. When it slips down the plane, it takes time ' $t_{1}$ '. When it rolls down the plane, it takes time $t_{2}$. The value of $\frac{t_{2}}{t_{1}}$ is $\sqrt{\frac{3}{x}}$. The value of $x$ will be___________. Solution: If disk slips on inclined plane, then it's acceleration $a_{1}=g \sin \theta$ $\mathrm{L}=\frac{1}{2} \mathrm{a}_{1} \mathrm{t}_{1}^{2}$ $\Rightarrow t_{1}=\sqrt{\frac{2 L}{a_{1}}}$ $\ldots ...
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Question: A $10 \Omega$ resistance is connected across $220 \mathrm{~V}-50 \mathrm{~Hz}$ AC supply. The time taken by the current to change from its maximum value to the rms value is:$2.5 \mathrm{~ms}$$1.5 \mathrm{~ms}$$3.0 \mathrm{~ms}$$4.5 \mathrm{~ms}$Correct Option: 1 Solution: $\Rightarrow \mathrm{i}=\mathrm{i}_{0} \sin \omega \mathrm{t}$ When $\mathrm{i}=\mathrm{i}_{0}$ $\mathrm{i}_{0}=\mathrm{i}_{0} \sin \omega \mathrm{t}_{1} \Rightarrow \omega \mathrm{t}_{1}=\frac{\pi}{2} \ldots$ (i) Whe...
Read More →The position of the centre of mass of a uniform semi-circular wire of radius
Question: The position of the centre of mass of a uniform semi-circular wire of radius ' $R$ ' placed in $\mathrm{x}-\mathrm{y}$ plane with its centre at the origin and the line joining its ends as $x$-axis is given by $\left(0, \frac{x R}{\pi}\right)$. Then, the value of $|x|$ is________________ Solution: COM of semi-circular ring is at $\frac{2 R}{\pi}$...
Read More →Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'.
Question: Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation when each thread makes a small angle '' with the vertical ?$\mathrm{x}=\left(\frac{\mathrm{q}^{2} l}{2 \pi \varepsilon_{0} \mathrm{mg}}\right)^{\frac{1}{2}}$$x=\left(\frac{q^{2} l}{2 \pi \varepsilon_{0} m g}\right)^{\frac{1}{3}}$$x=\left(\frac{q^{2} l^{2}}{2 \pi \varepsilon_{0} m^{2} g}\right)^{\frac{1}{3}}$$x=\left(\frac{q^{2} l^...
Read More →In the reported figure,
Question: In the reported figure, heat energy absorbed by a system in going through a cyclic process is_____ $\pi \mathrm{J}$. Solution: For complete cyclic process $\Delta \mathrm{U}=0$ $\therefore$ from $\Delta Q=\Delta U+W$ $=0+\mathrm{W}$ $\Delta \mathrm{Q}=\mathrm{W}$ $=$ Area $=\pi \mathrm{r}_{1} \cdot \mathrm{r}_{2}$ $=\pi \times\left(10 \times 10^{3}\right) \times\left(10 \times 10^{-3}\right)$ $\Delta \mathrm{Q}=100 \pi$ $\therefore$ Ans. $=100$...
Read More →Two ions having
Question: Two ions having same mass have charges in the ratio $1: 2$. They are projected normally in a uniform magnetic field with their speeds in the ratio $2: 3$. The ratio of the radii of their circular trajectories is:$1: 4$$4: 3$$3: 1$$2: 3$Correct Option: , 2 Solution: $\mathrm{R}=\frac{\mathrm{mv}}{\mathrm{qB}} \Rightarrow \frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}=\frac{\frac{\mathrm{mv}_{1}}{\mathrm{q}_{1} \mathrm{~B}}}{\frac{\mathrm{mv}_{2}}{\mathrm{q}_{2} \mathrm{~B}}}=\frac{\mathrm{v}_{1}...
Read More →In a given circuit diagram
Question: In a given circuit diagram, a $5 \mathrm{~V}$ zener diode along with a series resistance is connected across a $50 \mathrm{~V}$ power supply. The minimum value of the resistance required, if the maximum zener current is $90 \mathrm{~mA}$ will be $\Omega$. Solution: Voltage across $\mathrm{R}_{\mathrm{L}}=5 \mathrm{~V}$ $\Rightarrow \mathrm{i}_{2}=\frac{5}{\mathrm{R}_{\mathrm{L}}}$ Also voltage across $R=50-5=45$ volt By $v=i R \Rightarrow R=\frac{v}{i}=\frac{45}{i_{i}+i_{2}}$ $\mathrm{...
Read More →In the given potentiometer
Question: In the given potentiometer circuit arrangement, the balancing length $\mathrm{AC}$ is measured to be $250 \mathrm{~cm}$. When the galvanometer connection is shifted from point (1) to point (2) in the given diagram, the balancing length becomes $400 \mathrm{~cm}$. The ratio of the emf of two cells, $\frac{\varepsilon_{1}}{\varepsilon_{2}}$ is : $\frac{5}{3}$$\frac{8}{5}$$\frac{4}{3}$$\frac{3}{2}$Correct Option: 1 Solution: $\mathrm{E}_{1}=\mathrm{k} \ell_{1}$...(1) $\mathrm{E}_{1}+\math...
Read More →A body having specific charge
Question: A body having specific charge $8 \mu \mathrm{C} / \mathrm{g}$ is resting on a frictionless plane at a distance $10 \mathrm{~cm}$ from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of $100 \mathrm{~V} / \mathrm{m}$ is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be________ $\mathrm{s}$. Solution: $\mathrm{F}=\mathrm{ma}$ $\mathrm{qE}=\ma...
Read More →A 0.07 H inductor
Question: A 0.07 H inductor and a 12 resistor are connected in series to a 220 V, 50 Hz ac source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take $\pi$ as $\frac{22}{7}$ ]$8.8 \mathrm{~A}$ and $\tan ^{-1}\left(\frac{11}{6}\right)$$88 \mathrm{~A}$ and $\tan ^{-1}\left(\frac{11}{6}\right)$$0.88 \mathrm{~A}$ and $\tan ^{-1}\left(\frac{11}{6}\right)$$8.8 \mathrm{~A}$ and $\tan ^{-1}\left(\frac{6}{11}\right)$Correct Option: 1, S...
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