The velocity (v) and time (t) graph of a body in a straight line
Question: The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The point $S$ is at $4.333$ seconds. The total distance covered by the body in $6 \mathrm{~s}$ is : $12 \mathrm{~m}$$\frac{49}{4} \mathrm{~m}$$11 \mathrm{~m}$$\frac{37}{3} \mathrm{~m}$Correct Option: , 4 Solution: $\mathrm{OS}=4+\frac{1}{3}=\frac{13}{3}$ $\mathrm{SD}=2-\frac{1}{3}=\frac{5}{3}$ Area of $\mathrm{OABS}$ is $\mathrm{A}_{1}$ Area of $S C D$ is $A_{2}$ Distance $=\left|\mathrm{A}_...
Read More →A galvanometer is used in laboratory for detecting the null point
Question: A galvanometer is used in laboratory for detecting the null point in electrical experiments. If, on passing a current of $6 \mathrm{~mA}$ it produces a deflection of $2^{\circ}$, its figure of merit is close to:$3 \times 10^{-3} \mathrm{~A} / \mathrm{div}$$333^{\circ} \mathrm{A} / \mathrm{div}$$6 \times 10^{-3} \mathrm{~A} / \mathrm{div}$$666^{\circ} \mathrm{A} / \mathrm{div}$Correct Option: 1 Solution: Figure of Merit $=C=\frac{i}{\theta}$ $=\mathrm{C}=\frac{6 \times 10^{-3}}{2}=3 \ti...
Read More →Solve This follwing
Question: The quantities $\quad x=\frac{1}{\sqrt{\mu_{0} \in_{0}}}, y=\frac{E}{B} \quad$ and $\mathrm{z}=\frac{1}{\mathrm{CR}}$ are defined where C-capacitance, R-Resistance, $l$-length, E-Electric field, B-magnetic field and $\in_{0}, \mu_{0}$, free space permittivity and permeability respectively. Then :Only $x$ and $y$ have the same dimension$x, y$ and $z$ have the same dimensionOnly $x$ and $z$ have the same dimensionOnly $y$ and $z$ have the same dimensionCorrect Option: , 2 Solution: $x=\f...
Read More →Two different wires having lengths L_1 and L_2, and respective
Question: Two different wires having lengths $\mathrm{L}_{1}$ and $\mathrm{L}_{2}$, and respective temperature coefficient of linear expansion $\alpha_{1}$ and $\alpha_{2}$, are joined end-to-end. Then the effective temperature coefficient of linear expansion is :$4 \frac{\alpha_{1} \alpha_{2}}{\alpha_{1}+\alpha_{2}} \frac{\mathrm{L}_{2} \mathrm{~L}_{1}}{\left(\mathrm{~L}_{2}+\mathrm{L}_{1}\right)^{2}}$$2 \sqrt{\alpha_{1} \alpha_{2}}$$\frac{\alpha_{1}+\alpha_{2}}{2}$$\frac{\alpha_{1} \mathrm{~L}...
Read More →An massless equilateral triangle EFG of side
Question: An massless equilateral triangle EFG of side 'a' (As shown in figure) has three particles of mass $\mathrm{m}$ situated at its vertices. The moment of intertia of the system about the line EX perpendicular to $\mathrm{EG}$ in the plane of $\mathrm{EFG}$ is $\frac{\mathrm{N}}{20} \mathrm{ma}^{2}$ where $\mathrm{N}$ is an integer. The value of $\mathrm{N}$ is__________. Solution: $\mathrm{I}=0+\mathrm{m}\left(\frac{\mathrm{a}}{2}\right)^{2}+\mathrm{ma}^{2}$ $=\frac{5}{4} \mathrm{ma}^{2}$...
Read More →A block starts moving up an inclined plane of inclination
Question: A block starts moving up an inclined plane of inclination $30^{\circ}$ with an initial velocity of $v_{0}$. It comes back to its initial position with velocity $\frac{\mathrm{v}_{0}}{2}$. The value of the coefficient of kinetic friction between the block and the inclined plane is close to $\frac{\mathrm{I}}{1000}$, The nearest integer to $\mathrm{I}$ is_______. Solution: $\therefore \frac{1}{2} \mathrm{v}_{0} \frac{\mathrm{v}_{0}}{\mathrm{a}_{1}}=\frac{1}{2}\left(\frac{\mathrm{v}_{0}}{...
Read More →If minimum possible work is done by a refrigerator
Question: If minimum possible work is done by a refrigerator in converting 100 grams of water at $0^{\circ} \mathrm{C}$ to ice, how much heat (in calories) is released to the surrounding at temperature $27^{\circ} \mathrm{C}$ (Latent heat of ice $=80 \mathrm{Cal} /$ gram to the nearest integer? Solution: $w+Q_{1}=Q_{2}$ $w=Q_{2}-Q_{1}$ C.O.P. $=\frac{Q_{1}}{w}=\frac{Q_{1}}{Q_{2}-Q_{1}}=\frac{273}{300-273}=\frac{Q_{1}}{W}$ $\mathrm{w}=\frac{27}{273} \times 80 \times 100 \times 4.2$ $\mathrm{Q}_{2...
Read More →In an experiment to verify Stokes law, a small spherical ball
Question: In an experiment to verify Stokes law, a small spherical ball of radius $\mathrm{r}$ and density $\rho$ falls under gravity through a distance $\mathrm{h}$ in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of $\mathrm{h}$ is proportional to : (ignore viscosity of air)$\mathrm{r}$$r^{4}$$\mathrm{r}^{3}$$\mathrm{r}^{2}$Correct Option: , 2 Solution: After falling through ...
Read More →A galvanometer coil has 500 turns and each turn
Question: A galvanometer coil has 500 turns and each turn has an average area of $3 \times 10^{-4} \mathrm{~m}^{2}$. If a torque of $1.5 \mathrm{Nm}$ is required to keep this coil parallel to magnetic field when a current of $0.5 \mathrm{~A}$ is flowing through it, the strength of the field (in T) is_______. Solution: $\vec{\tau}=\overrightarrow{\mathrm{m}} \times \overrightarrow{\mathrm{B}}$ $\tau=\mathrm{NI} \times \mathrm{A} \times \mathrm{B}$ $105=500 \times 3 \times 10^{-4} \times \frac{1}{...
Read More →When an object is kept at a distance of
Question: When an object is kept at a distance of $30 \mathrm{~cm}$ from a concave mirror, the image is formed at a distance of $10 \mathrm{~cm}$ from the mirror. If the object is moved with a speed of $9 \mathrm{cms}^{-1}$, the speed (in $\mathrm{cms}^{-1}$ ) with which image moves at that instant is_______. Solution: $\left|\left(\frac{\mathrm{dv}}{\mathrm{dt}}\right)\right|=\left|\frac{\mathrm{v}^{2}}{4^{2}}\right| \frac{\mathrm{du}}{\mathrm{dt}} \mid$ $=\left(\frac{10}{30}\right) 2 \times 9=...
Read More →In the circuit shown, charge on the
Question: In the circuit shown, charge on the $5 \mu \mathrm{F}$ capacitor is : $5.45 \mu \mathrm{C}$$16.36 \mu \mathrm{C}$$10.90 \mu \mathrm{C}$$18.00 \mu \mathrm{C}$Correct Option: 2, Solution: Now, using junction analysis We can say, $\quad q_{1}+q_{2}+q_{3}=0$ $2(x-6)+4(x-6)+5(x)=0$ $\mathrm{x}=\frac{36}{11} \quad \mathrm{q}_{3}=\frac{36(5)}{11}=\frac{180}{11}$ $\mathrm{q}_{3}=16.36 \mu \mathrm{C}$...
Read More →Solve this following
Question: Initially a gas of diatomic molecules is contained in a cylinder of volume $\mathrm{V}_{1}$ at a pressure $\mathrm{P}_{1}$ and temperature $250 \mathrm{~K}$. Assuming that $25 \%$ of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature $2000 \mathrm{~K}$, when contained in a volume $2 \mathrm{~V}_{1}$ is given by $P_{2}$. The ratio $P_{2} / P_{1}$ is. Solution: $\mathrm{PV}=\mathrm{nRT}$ $\mathrm{P}_{1} \mathrm{~V}_{1}=\mat...
Read More →The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density
Question: The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is $\left(\frac{x}{100}\right) \%$. If the relative errors in measuring the mass and the diameter are $6.0 \%$ and $1.5 \%$ respectively, the value of $x$ is. Solution: $\rho=\frac{\mathrm{M}}{\mathrm{V}}=\frac{\mathrm{M}}{\frac{4}{3} \pi\left(\frac{\mathrm{D}}{2}\right)^{3}}$ $\rho=\frac{6}{\pi} \mathrm{M} \mathrm{D}^{-3}$ taking log $\ell \mathrm{n}...
Read More →Prove the following
Question: A uniform rod of length ' $l$ ' is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed $\omega$ the rod makes an angle $\theta$ with it (see figure). To find $\theta$ equate the rate of change of angular momentum (direction going into the paper) $\frac{m \ell^{2}}{12} \omega^{2} \sin \theta \cos \theta$ about the centre of mass (CM) to the torque provided by the horizontal and vertical forces $\mathrm{F}_{\mathrm{H}}$ and $\mathr...
Read More →A ring is hung on a nail. It can oscillate, without slipping
Question: A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period $T_{1}$ and, (ii) back and forth in a direction perpendicular to its plane, with a period $\mathrm{T}_{2}$. the ratio $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}$ will be :$\frac{2}{\sqrt{3}}$$\frac{\sqrt{2}}{3}$$\frac{2}{3}$$\frac{3}{\sqrt{2}}$Correct Option: 1 Solution: Moment of inertia in case (i) is $\mathrm{I}_{1}$ Moment of inertia in case (ii) is $\mathrm{I}_{2}$ $\mathrm{I}_...
Read More →Solve this following
Question: Suppose that intensity of a laser is $\left(\frac{315}{\pi}\right) \mathrm{W} / \mathrm{m}^{2}$. The rms electric field, in units of $\mathrm{V} / \mathrm{m}$ associated with this source is close to the nearest integer is $\left(\epsilon_{0}=8.86 \times 10^{-12} \mathrm{C}^{2} \mathrm{Nm}^{-2} ; \mathrm{c}=3 \times 10^{8} \mathrm{~ms}^{-1}\right)$ Solution: $\mathrm{I}=\epsilon_{0} \mathrm{E}_{\mathrm{rms}}^{2} \mathrm{C}$ $\mathrm{E}_{\mathrm{rms}}^{2}=\frac{\mathrm{I}}{\epsilon_{0} \...
Read More →A calorimeter of water equivalent 20g contains 180g of water
Question: A calorimeter of water equivalent $20 \mathrm{~g}$ contains $180 \mathrm{~g}$ of water at $25^{\circ} \mathrm{C}$. 'm' grams of steam at $100^{\circ} \mathrm{C}$ is mixed in it till the temperature of the mixure is $31^{\circ} \mathrm{C}$. The value of ' $\mathrm{m}$ ' is close to (Latent heat of water $=540 \mathrm{cal} \mathrm{g}^{-1}$, specific heat of water $=1 \mathrm{cal} \mathrm{g}^{-1}{ }^{\circ} \mathrm{C}^{-1}$ )$2.6$24$3.2$Correct Option: , 2 Solution: $\frac{\mathrm{Cal}}{2...
Read More →A Young's doublc-slit experiment is performed using
Question: A Young's doublc-slit experiment is performed using monochromatic light of wavelength $\lambda$. The intensity of light at a point on the screen, where the path difference is $\lambda$, is $\mathrm{K}$ units. The intensity of light at a point where the path difference is $\mathrm{A} \frac{\lambda}{6}$ is given by $\frac{\mathrm{nK}}{12}$, where $\mathrm{n}$ is an integer. The value of $\mathrm{n}$ is Solution: $\mathrm{I}_{\max }=\mathrm{k}$ $\mathrm{I}_{1}=\mathrm{I}_{2}=\mathrm{K} / ...
Read More →In a scries LR circuit, power of
Question: In a scries LR circuit, power of $400 \mathrm{~W}$ is dissipated from a source of $250 \mathrm{~V}, 50 \mathrm{~Hz}$. The power factor of the circuit is $0.8$. In order to bring the power factor to unity, a capacitor of value $\mathrm{C}$ is added in series to the $\mathrm{L}$ and $\mathrm{R}$. Taking the value of $\mathrm{C}$ as $\left(\frac{\mathrm{n}}{3 \pi}\right) \mu \mathrm{F}$, then value of $\mathrm{n}$ is Solution: $P=\frac{E_{\text {rms }}^{2}}{Z} \cos \phi$ $400=\frac{(250)^...
Read More →Two bodies of the same mass are moving with the same speed, but in different directions in a plane.
Question: Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial speed. The angle between the initial velocities of the two bodies (in degree) is. Solution: Momentum conservation along $x$ $2 \mathrm{mv}_{0} \cos \theta=2 \mathrm{~m} \frac{\mathrm{v}_{0}}{2}$ $\cos \theta=\frac{1}{2}$ $\theta=60$ Angle is $2 \theta=120$ Ans. $120.0...
Read More →The output characteristics of a transistor
Question: The output characteristics of a transistor is shown in the figure. When $\mathrm{V}_{\mathrm{CE}}$ is $10 \mathrm{~V}$ and $1_{\mathrm{C}}=4.0 \mathrm{~mA}$, then value of $\beta_{\mathrm{ac}}$ is Solution: $\Delta \mathrm{I}_{\mathrm{B}}=(30-20)=10 \mu \mathrm{A}$ $\Delta \mathrm{I}_{\mathrm{C}}=(4.5-3) \mathrm{mA}=1.5 \mathrm{~mA}$ $\beta_{\mathrm{ac}}=\frac{\Delta \mathrm{I}_{\mathrm{C}}}{\Delta \mathrm{I}_{\mathrm{B}}}=\frac{1.5 \mathrm{~mA}}{10 \mu \mathrm{A}}=150$ $\beta_{\mathrm...
Read More →Two sources of light emit X-rays of wavelength
Question: Two sources of light emit X-rays of wavelength $1 \mathrm{~nm}$ and visible light of wavelength $500 \mathrm{~nm}$, respectively. Both the sources emit light of the same power $200 \mathrm{~W}$. The ratio of the number density of photons of $\mathrm{X}$-rays to the number densitty of photons of the visible light of the given wavelengths is :$\frac{1}{500}$500250$\frac{1}{250}$Correct Option: 1 Solution: $P=\frac{n h c}{\lambda t}$ $\therefore \frac{\mathrm{n}_{1}}{\mathrm{n}_{2}}=\frac...
Read More →A radioactive nucleus decays by two different processes.
Question: A radioactive nucleus decays by two different processes. The half life for the first process is $10 \mathrm{~s}$ and that for the second is $100 \mathrm{~s}$. the effective half life of the nucleus is close to:$9 \mathrm{sec}$$55 \mathrm{sec}$$6 \mathrm{sec}$$12 \mathrm{sec}$Correct Option: 1, Solution: $\frac{1}{\mathrm{~T}_{\text {eff }}}=\frac{1}{\mathrm{~T}_{1}}+\frac{1}{\mathrm{~T}_{2}}$ $\mathrm{T}_{\mathrm{eff}}=\frac{\mathrm{T}_{1} \mathrm{~T}_{2}}{\mathrm{~T}_{1}+\mathrm{T}_{2...
Read More →The centre of mass of a solid hemisphere of radius
Question: The centre of mass of a solid hemisphere of radius $8 \mathrm{~cm}$ is $X \mathrm{~cm}$ from the centre of the flat surface. Then value of $x$ is Solution: $x=\frac{3 R}{8}=3 \mathrm{~cm}$ $x=3$...
Read More →Solve this following
Question: A part of a complete circuit is shown in the figure. At some instant, the value of current I is $1 \mathrm{~A}$ and it is decreasing at a rate of $10^{2} \mathrm{~A} \mathrm{~s}^{-1}$. The value of the potential difference $\mathrm{V}_{\mathrm{P}}-\mathrm{V}_{\mathrm{Q}}$, (in volts) at that instant, is. Solution: $\frac{\text { Ldi }}{\text { dt }}=5$ $\mathrm{V}_{\mathrm{P}}-5-30+2 \times 1=\mathrm{VQ}$ $\mathrm{V}_{\mathrm{P}}-\mathrm{V}_{\mathrm{Q}}=33$ volt Ans. $33.00$...
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