A nucleus of mass M emits
Question: A nucleus of mass $M$ emits $\gamma$-ray photon of frequency ' $v$ '. The loss of internal energy by the nucleus is: [Take 'c' as the speed of electromagnetic wave]hv0$\mathrm{h} v\left[1-\frac{\mathrm{hv}}{2 \mathrm{Mc}^{2}}\right]$$\mathrm{h} v\left[1+\frac{\mathrm{hv}}{2 \mathrm{Mc}^{2}}\right]$Correct Option: , 2 Solution: Energy of $\gamma$ ray $\left[\mathrm{E}_{\gamma}\right]=\mathrm{h} v$ Momentum of $\gamma$ ray $\left[\mathrm{P}_{\gamma}\right]=\frac{\mathrm{h}}{\lambda}=\fra...
Read More →In the given figure,
Question: In the given figure, there is a circuit of potentiometer of length $\mathrm{AB}=10 \mathrm{~m}$. The resistance per unit length is $0.1 \Omega$ per $\mathrm{cm}$. Across $\mathrm{AB}$, a battery of emf $E$ and internal resistance ' $r$ ' is connected. The maximum value of emf measured by this potentiometer is : $5 \mathrm{~V}$$2.25 \mathrm{~V}$$6 \mathrm{~V}$$2.75 \mathrm{~V}$Correct Option: 1 Solution: Max. voltage that can be measured by this potentiometer will be equal to potential ...
Read More →In the reported figure, a capacitor is formed by
Question: In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be : (Given area of plate = A) $\frac{15}{34} \frac{\mathrm{K} \varepsilon_{0} \mathrm{~A}}{\mathrm{~d}}$$\frac{15}{6} \frac{\mathrm{K}_{0} \mathrm{~A}}{\mathrm{~d}}$$\frac{25}{6} \frac{\mathrm{K} \varepsilon_{0} \mathrm{~A}}{\mathrm{~d}}$$\frac{9}{6} \frac{K \varepsilon_{0} A}{d}$Correct Option: 1 Solu...
Read More →Choose the correct option :
Question: Choose the correct option : True dip is not mathematically related to apparent dip.True dip is less than apparent dip.True dip is always greater than the apparent dip.True dip is always equal to apparent dip.Correct Option: , 2 Solution: If apparent dip circle is at an angle $\alpha$ with true dip circle then Apparent dip circle...
Read More →A capacitor of capacitance C=1 uF is suddenly connected to a battery of 100 volt
Question: A capacitor of capacitance $\mathrm{C}=1 \mu \mathrm{F}$ is suddenly connected to a battery of 100 volt through a resistance $R=100 \Omega$. The time taken for the capacitor to be charged to get $50 \mathrm{~V}$ is : $[$ Take $\ln 2=0.69]$$1.44 \times 10^{-4} \mathrm{~s}$$3.33 \times 10^{-4} \mathrm{~s}$$0.69 \times 10^{-4} \mathrm{~s}$$0.30 \times 10^{-4} \mathrm{~s}$Correct Option: , 3 Solution: $\mathrm{V}=\mathrm{V}_{0}\left(1-\mathrm{e}^{-\frac{\mathrm{t}}{R C}}\right)$ $50=100\le...
Read More →Solve this following
Question: A bullet of ' $4 \mathrm{~g}^{\prime}$ mass is fired from a gun of mass $4 \mathrm{~kg}$. If the bullet moves with the muzzle speed of $50 \mathrm{~ms}^{-1}$, the impulse imparted to the gun and velocity of recoil of gun are:$0.4 \mathrm{~kg} \mathrm{~ms}^{-1}, 0.1 \mathrm{~ms}^{-1}$$0.2 \mathrm{~kg} \mathrm{~ms}^{-1}, 0.05 \mathrm{~ms}^{-1}$$0.2 \mathrm{~kg} \mathrm{~ms}^{-1}, 0.1 \mathrm{~ms}^{-1}$$0.4 \mathrm{~kg} \mathrm{~ms}^{-1}, 0.05 \mathrm{~ms}^{-1}$Correct Option: , 2 Solutio...
Read More →A linearly polarized electromagnetic
Question: A linearly polarized electromagnetic wave in vacuum is $\mathrm{E}=3.1 \cos \left[(1.8) \mathrm{z}-\left(5.4 \times 10^{6}\right) \mathrm{t}\right] \hat{\mathrm{i}} \mathrm{N} / \mathrm{C}$ is incident normally on a perfectly reflecting wall at $\mathrm{z}=\mathrm{a}$. Choose the correct optionThe wavelength is $5.4 \mathrm{~m}$The frequency of electromagnetic wave is $54 \times 10^{4} \mathrm{~Hz}$The transmitted wave will be $3.1 \cos \left[(1.8) \mathrm{z}-\left(5.4 \times 10^{6}\ri...
Read More →A deuteron and an alpha particle having equal kinetic energy
Question: A deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let $r_{d}$ and $r_{\alpha}$ be their respective radii of circular path. The value of $\frac{r_{d}}{r_{\alpha}}$ is equal to :$\frac{1}{\sqrt{2}}$$\sqrt{2}$12Correct Option: , 2 Solution: $r=\frac{m v}{q B}=\frac{\sqrt{2 m k}}{q B}$ $\frac{\mathrm{r}_{\mathrm{d}}}{\mathrm{r}_{\alpha}}=\sqrt{\frac{\mathrm{m}_{\mathrm{d}}}{\mathrm{m}_{\alpha}} \frac{\mathrm{q}_{\mathrm{\alpha}}}{\mathr...
Read More →Statement I : The ferromagnetic property depends on temperature. At high temperature, ferromagnet becomes paramagnet.
Question: Statement I : The ferromagnetic property depends on temperature. At high temperature, ferromagnet becomes paramagnet. Statement II : At high temperature, the domain wall area of a ferromagnetic substance increases. In the light of the above statements, choose the most appropriate answer from the options given bclow :Statement I is true but Statement II is falseBoth Statement I and Statement II are trueBoth Statement I and Statement II are falseStatement I is false but Statement II is t...
Read More →Two different metal bodies
Question: Two different metal bodies $A$ and $B$ of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is : $\frac{8}{3}$$\frac{3}{8}$$\frac{3}{4}$$\frac{4}{3}$Correct Option: , 2 Solution: $\left(\frac{\Delta \mathrm{Q}}{\Delta \mathrm{t}}\right)_{\mathrm{A}}=\left(\frac{\Delta \mathrm{Q}}{\Delta \mathrm{t}}\right)_{\mathrm{B}}$ $\mathrm{mS}_{\mathrm...
Read More →Three objects A, B and C are kept in a straight line on a frictionless horizontal surface.
Question: Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2 m and 2 m respectively. A moves towards B with a speed of 9 m/s and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. All motions occur along same straight line. The final speed of C is : 6 m/s9 m/s4 m/s3 m/sCorrect Option: , 4 Solution: Sol. Collision between A and B $\mathrm{m} \times 9=\mathrm{mv}_{1}+2 \mathrm{mv}...
Read More →If A and B are two vectors satisfying the relation
Question: If $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ are two vectors satisfying the relation $\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}}=|\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}|$. Then the value of $|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}|$ will be :$\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}}$$\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}+\sqrt{2} \mathrm{AB}}$$\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}+2 \mathrm{AB}}$$\sqrt{\mathrm{A}...
Read More →Three objects A, B and C are kept in a straight line on a frictionless horizontal surface.
Question: Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2 m and 2 m respectively. A moves towards B with a speed of 9 m/s and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. All motions occur along same straight line. The final speed of C is : 6 m/s9 m/s4 m/s3 m/sCorrect Option: , 4 Solution: Sol. Collision between A and B $\mathrm{m} \times 9=\mathrm{mv}_{1}+2 \mathrm{mv}...
Read More →In the Young's double slit experiment,
Question: In the Young's double slit experiment, the distance between the slits varies in time as $\mathrm{d}(\mathrm{t})=\mathrm{d}_{0}+\mathrm{a}_{0} \sin \omega \mathrm{t} ;$ where $\mathrm{d}_{0}, \omega$ and $\mathrm{a}_{0}$ are constants. The difference between the largest fringe width and the smallest fringe width obtained over time is given as :$\frac{2 \lambda D\left(d_{0}\right)}{\left(d_{0}^{2}-a_{0}^{2}\right)}$$\frac{2 \lambda \mathrm{Da}_{0}}{\left(\mathrm{~d}_{0}^{2}-\mathrm{a}_{0...
Read More →Solve this following
Question: A ray of light passes from a denser medium to a rarer medium at an angle of incidence $i$. The reflected and refracted rays make an angle of $90^{\circ}$ with each other. The angle of reflection and refraction are respectively $r$ and $r^{\prime}$. The critical angle is given by : $\sin ^{-1}(\operatorname{cotr})$$\tan ^{-1}(\sin i)$$\sin ^{-1}\left(\operatorname{tanr}^{\prime}\right)$$\sin ^{-1}(\tan r)$Correct Option: , 4 Solution: $r+r^{\prime}+90^{\circ}=180^{\circ} \Rightarrow r^{...
Read More →The amount of heat needed to raise the temperature
Question: The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from $0^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$ when no work is done is_______ . $R$ is the universal gas constant)$250 R$$750 \mathrm{R}$$175 \mathrm{R}$$500 \mathrm{R}$Correct Option: , 4 Solution: $\Delta \mathrm{Q}=\Delta \mathrm{U}+\Delta \mathrm{W}$ Here $\Delta W=0$ $\Delta \mathrm{Q}=\Delta \mathrm{U}=\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}$ $\Delta Q=4 \times \frac{5 R}{2}(50)=500 \...
Read More →Two billiard balls of equal mass
Question: Two billiard balls of equal mass $30 \mathrm{~g}$ strike a rigid wall with same speed of $108 \mathrm{kmph}$ (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball ' $a$ ' and ball ' $b$ ' by the wall along ' $X$ ' direction is : $1: 1$$\sqrt{2}: 1$$2: 1$$1: \sqrt{2}$Correct Option: , 2 Solution: Impulse $=$ change in momentum Ball (a) $|\overrightarrow{\Delta \mathrm{p}}|=2 \mathrm{mu}=\mathrm{J}_...
Read More →Choose the correct answer from the options given below :
Question: Choose the correct answer from the options given below :(a)(ii), (b)(iii), (c) (i), (d)(iv)(a)(ii), (b)(i), (c) (iii), (d)(iv)(a)(iii), (b)(iv), (c) (ii), (d)(i)(a)(iii), (b)(iv), (c) (i), (d)(ii)Correct Option: , 3 Solution:...
Read More →Choose the correct answer from the options given below :
Question: Choose the correct answer from the options given below :(a)(ii), (b)(iii), (c) (i), (d)(iv)(a)(ii), (b)(i), (c) (iii), (d)(iv)(a)(iii), (b)(iv), (c) (ii), (d)(i)(a)(iii), (b)(iv), (c) (i), (d)(ii)Correct Option: , 3 Solution:...
Read More →The half-life of
Question: The half-life of ${ }^{198} \mathrm{Au}$ is 3 days. If atomic weight of ${ }^{198} \mathrm{Au}$ is $198 \mathrm{~g} / \mathrm{mol}$ then the activity of $2 \mathrm{mg}$ of ${ }^{198} \mathrm{Au}$ is [in disintegration/second] :$2.67 \times 10^{12}$$6.06 \times 10^{18}$$32.36 \times 10^{12}$$16.18 \times 10^{12}$Correct Option: , 4 Solution: $\mathrm{A}=\lambda \mathrm{N}$ $\lambda=\frac{\ln 2}{t_{1 / 2}}=\frac{\ln 2}{3 \times 24 \times 60 \times 60} \mathrm{sec}^{-1}=2.67 \times 10^{-6...
Read More →Two wires of same length
Question: Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are $Y_{1}$ and $Y_{2}$. The combination behaves as a single wire then its Young's modulus is :$Y=\frac{2 Y_{1} Y_{2}}{3\left(Y_{1}+Y_{2}\right)}$$\mathrm{Y}=\frac{2 \mathrm{Y}_{1} \mathrm{Y}_{2}}{\mathrm{Y}_{1}+\mathrm{Y}_{2}}$$Y=\frac{Y_{1} Y_{2}}{2\left(Y_{1}+Y_{2}\right)}$$\mathrm{Y}=\frac{\mathrm{Y}_{1} \mathrm{Y}_{2}}{\mathrm{Y}_{1}+\mathrm{Y}_{2}}$Correct O...
Read More →Solve this following
Question: $T_{0}$ is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to $\frac{1}{16}$ times of its initial value, the modified time period is:$\mathrm{T}_{0}$$8 \pi \mathrm{T}_{0}$$4 \mathrm{~T}_{0}$$\frac{1}{4} T_{0}$Correct Option: , 4 Solution: $\mathrm{T}_{0}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}}}$ New time period $\mathrm{T}=2 \pi \sqrt{\frac{\ell / 16}{\mathrm{~g}}}=\frac{2 \pi}{4} \sqrt{\frac{\ell}{\mathrm{g}}}$ $\mathrm{T}=\frac{\mathrm{T}_{0}}{4}...
Read More →A ray of laser of a wavelength
Question: A ray of laser of a wavelength $630 \mathrm{~nm}$ is incident at an angle of $30^{\circ}$ at the diamond-air interface. It is going from diamond to air. The refractive index of diamond is $2.42$ and that of air is 1 . Choose the correct option.angle of refraction is $24.41^{\circ}$angle of refraction is $30^{\circ}$refraction is not possibleangle of refraction is $53.4^{\circ}$Correct Option: , 3 Solution: $\sin \theta_{C}=\frac{1}{\mu}=\frac{1}{2 \mu_{2}}\sin \theta_{C}$ $\sin \theta\...
Read More →A monoatomic ideal gas,
Question: A monoatomic ideal gas, initially at temperature $T_{1}$ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $\mathrm{T}_{2}$ by releasing the piston suddenly. If $l_{1}$ and $l_{2}$ are the lengths of the gas column, before and after the expansion respectively, then the value of $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}$ will be :$\left(\frac{l_{1}}{l_{2}}\right)^{\frac{2}{3}}$$\left(\frac{l_{2}}{l_{1}}\right)^{\frac{2...
Read More →A porter lifts a heavy suitcase of mass
Question: A porter lifts a heavy suitcase of mass $80 \mathrm{~kg}$ and at the destination lowers it down by a distance of $80 \mathrm{~cm}$ with a constant velocity. Calculate the workdone by the porter in lowering the suitcase. $\left(\right.$ take $\left.\mathrm{g}=9.8 \mathrm{~ms}^{-2}\right)$$-62720.0 \mathrm{~J}$$-627.2 \mathrm{~J}$$+627.2 \mathrm{~J}$$784.0 \mathrm{~J}$Correct Option: , 2 Solution: $\mathrm{W}_{\text {Porter }}+\mathrm{W}_{\mathrm{mg}}=\Delta \mathrm{K} \cdot \mathrm{E} ....
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