Assume that a neutron breaks into a proton and an electron.
Question: Assume that a neutron breaks into a proton and an electron. The energy released during this process is: (Mass of neutron $=1.6747 \times 10^{-27} \mathrm{~kg}$ Mass of proton $=1.6725 \times 10^{-27} \mathrm{~kg}$ Mass of electron $=9 \times 10^{-31} \mathrm{~kg}$ )$5.4 \mathrm{MeV}$$0.73 \mathrm{MeV}$$7.10 \mathrm{MeV}$$6.30 \mathrm{MeV}$Correct Option: , 2 Solution:...
Read More →Statement-1: A nucleus having energy
Question: Statement-1: A nucleus having energy $\mathrm{E}_{1}$ decays $\beta^{-}$emission to daughter nucleus having energy $\mathrm{E}_{2}$, but the $\beta^{-}$rays are emitted with a continuous energy spectrum having end point energy $\mathrm{E}_{1}-\mathrm{E}_{2}$. Statement-1: To conserve energy and momentum in $\beta$-decay at least three particles must take part in the transformation.Statement- 1 is incorrect, statement-2 is correctStatement-1 is correct, statement-2 is incorrectStatement...
Read More →Three concentric metal shells A ,
Question: Three concentric metal shells $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ of respective radii $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}(\mathrm{a}\mathrm{b}\mathrm{c})$ have surface charge densities $+\sigma,-\sigma$ and $+\sigma$ respectively. The potential of shell B is :-$\frac{\sigma}{\varepsilon_{0}}\left[\frac{a^{2}-b^{2}}{b}+c\right]$$\frac{\sigma}{\varepsilon_{0}}\left[\frac{\mathrm{b}^{2}-\mathrm{c}^{2}}{\mathrm{~b}}+\mathrm{a}\right]$$\frac{\sigma}{\varepsilon_{0}}\left[\frac{\m...
Read More →Solve this following
Question: A force $\overrightarrow{\mathrm{F}}=(5 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}) \mathrm{N}$ is applied over a particle which displaces it from its origin to the point $\overrightarrow{\mathrm{r}}=(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}) \mathrm{m}$. The work done on the particle in joules is- $-7 \mathrm{~J}$$+7 \mathrm{~J}$$+10 \mathrm{~J}$$+13 \mathrm{~J}$Correct Option: , 2 Solution:...
Read More →After absorbing a slowly moving neutron of mass
Question: After absorbing a slowly moving neutron of mass $\mathrm{m}_{\mathrm{N}}($ momentum $\sim 0)$ a nucleus of mass $\mathrm{M}$ breaks into two nuclei of masses $\mathrm{m}_{1}$ and $5 \mathrm{~m}_{1}\left(6 \mathrm{~m}_{1}=\mathrm{M}+\mathrm{m}_{\mathrm{N}}\right)$, respectively. If the de Broglie wavelength of the nucleus with mass $m_{1}$ is $\lambda$, then de Broglie wavelength of the other nucleus will be:- $25 \lambda$$5 \lambda$$\frac{\lambda}{5}$$\lambda$Correct Option: , 4 Soluti...
Read More →An electric dipole has a fixed dipole moment
Question: An electric dipole has a fixed dipole moment $\overrightarrow{\mathrm{p}}$, which makes angle $\theta$ with respect to $\mathrm{x}$-axis. When subjected to an electric field $\overrightarrow{\mathrm{E}}_{1}=\mathrm{E} \hat{\mathrm{i}}$, it experiences a torque $\overrightarrow{\mathrm{T}}_{1}=\tau \hat{\mathrm{k}}$. When subjected to another electric field $\overrightarrow{\mathrm{E}}_{2}=\sqrt{3} \mathrm{E}_{1} \hat{\mathrm{j}}$ it experiences torque $\overrightarrow{\mathrm{T}}_{2}=-...
Read More →The variation of acceleration due
Question: The variation of acceleration due to gravity $g$ with distance d from centre of the earth is best represented by ( $\mathrm{R}=$ Earth's radius) :-Correct Option: , 2 Solution:...
Read More →A radioactive nucleus initial mass number A and atomic number Z
Question: A radioactive nucleus (initial mass number $A$ and atomic number $Z$ ) emits $3 \alpha$-particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be:- $\frac{\mathrm{A}-\mathrm{Z}-4}{\mathrm{Z}-2}$$\frac{A-Z-8}{Z-4}$$\frac{\mathrm{A}-\mathrm{Z}-4}{\mathrm{Z}-8}$$\frac{\mathrm{A}-\mathrm{Z}-12}{\mathrm{Z}-4}$Correct Option: , 3 Solution:...
Read More →The region between two concentric spheres of radii 'a' and 'b',
Question: The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density $\rho=\frac{\mathrm{A}}{\mathrm{r}}$, where $\mathrm{A}$ is a constant and $\mathrm{r}$ is the distance from the centre. At the centre of the spheres is a point charge $Q$. The value of A such that the electric field in the region between the spheres will be constant, is :- $\frac{2 Q}{\pi a^{2}}$$\frac{\mathrm{Q}}{2 \pi \mathrm{a}^{2}}$$\frac{Q}{2 \pi\left(b^{2}-a^{2}\r...
Read More →A satellite is reolving in a
Question: A satellite is reolving in a circular orbit at a height ' $h$ ' from the earth's surface (radius of earth $\mathrm{R} ; \mathrm{h}\mathrm{R}$ ). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to : (Neglect the effect of atmosphere).$\sqrt{g R}(\sqrt{2}-1)$$\sqrt{2 g R}$$\sqrt{\mathrm{gR}}$$\sqrt{g R / 2}$Correct Option: 1 Solution:...
Read More →From a solid sphere of mass
Question: From a solid sphere of mass $\mathrm{M}$ and radius $\mathrm{R}$, a spherical portion of radius $\frac{\mathrm{R}}{2}$ is removed, as shown in the figure. Taking gravitational potential $\mathrm{V}=0$ at $\mathrm{r}=\infty$, the potential at the centre of the cavity thus formed is : ( $\mathrm{G}=$ gravitational constant $)$ $\frac{-2 \mathrm{GM}}{3 \mathrm{R}}$$\frac{-2 \mathrm{GM}}{\mathrm{R}}$$\frac{-\mathrm{GM}}{2 \mathrm{R}}$$\frac{-\mathrm{GM}}{\mathrm{R}}$Correct Option: , 4 Sol...
Read More →The binding energy per nucleon for the parent nucleus is
Question: The binding energy per nucleon for the parent nucleus is $\mathrm{E}_{1}$ an that for the daughter nuclei is $\mathrm{E}_{2}$. Then:- $\mathrm{E}_{1}=2 \mathrm{E}_{2}$$\mathrm{E}_{2}=2 \mathrm{E}_{1}$$\mathrm{E}_{1}\mathrm{E}_{2}$$\mathrm{E}_{2}\mathrm{E}_{1}$Correct Option: , 4 Solution: Because energy is releasing $\Rightarrow$ Binding energy per nucleon of product $$ that of parent $\Rightarrow \mathrm{E}_{2}\mathrm{E}_{1}$....
Read More →Assume that an electric field
Question: Assume that an electric field $\overrightarrow{\mathrm{E}}=30 \mathrm{x}^{2} \hat{\mathrm{i}}$ exists in space. Then the potential difference $\mathrm{V}_{\mathrm{A}}-\mathrm{V}_{\mathrm{O}}$, where $\mathrm{V}_{\mathrm{O}}$ is the potential at the origin and $\mathrm{V}_{\mathrm{A}}$ the potential at $\mathrm{x}=2 \mathrm{~m}$ is :-$-80 \mathrm{~J}$$80 \mathrm{~J}$120 J- 120 JCorrect Option: 1 Solution:...
Read More →Four particles, each of mass
Question: Four particles, each of mass $\mathrm{M}$ and equidistant from each other, move along a circle of radius $\mathrm{R}$ under the action of their mutual gravitational attraction. The speed of each particle is :$\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}(1+2 \sqrt{2})}$$\frac{1}{2} \sqrt{\frac{\mathrm{GM}}{\mathrm{R}}(1+2 \sqrt{2})}$$\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}$$\sqrt{2 \sqrt{2} \frac{\mathrm{GM}}{\mathrm{R}}}$Correct Option: , 2 Solution:...
Read More →The speed of daughter nuclei is
Question: The speed of daughter nuclei is :-$c \sqrt{\frac{\Delta m}{M+\Delta m}}$$c \frac{\Delta m}{M+\Delta m}$$\mathrm{c} \cdot \sqrt{\frac{2 \Delta \mathrm{m}}{\mathrm{M}}}$$c \sqrt{\frac{\Delta m}{M}}$Correct Option: , 3 Solution:...
Read More →A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure.
Question: A charge $\mathrm{Q}$ is uniformly distributed over a long rod $\mathrm{AB}$ of length $\mathrm{L}$ as shown in the figure. The electric potential at the point $\mathrm{O}$ lying at a distance $\mathrm{L}$ from the end $\mathrm{A}$ is :-- $\frac{Q}{8 \pi \epsilon_{0} L}$$\frac{3 \mathrm{Q}}{4 \pi \epsilon_{0} \mathrm{~L}}$$\frac{Q}{4 \pi \epsilon_{0} L \ln 2}$$\frac{\mathrm{Q} \ln 2}{4 \pi \epsilon_{0} \mathrm{~L}}$Correct Option: , 4 Solution:...
Read More →What is the minimum
Question: What is the minimum energy required to launch a satellite of mass $\mathrm{m}$ from the surface of a planet of mass $\mathrm{M}$ and radius $\mathrm{R}$ in a circular orbit at an altitude of $2 \mathrm{R}$ ?$\frac{5 \mathrm{GmM}}{6 \mathrm{R}}$$\frac{2 G m M}{3 R}$$\frac{\mathrm{GmM}}{2 \mathrm{R}}$$\frac{\mathrm{GmM}}{3 \mathrm{R}}$Correct Option: 1 Solution:...
Read More →The mass of a spaceship
Question: The mass of a spaceship is $1000 \mathrm{~kg}$. It is to be launched from the earth's surface out into free space. The value of ' $g$ ' and ' $\mathrm{R}$ ' (radius of earth) are $10 \mathrm{~m} / \mathrm{s}^{2}$ and $6400 \mathrm{~km}$ respectively. The required energy for this work will be :-$6.4 \times 10^{10}$ Joules$6.4 \times 10^{11}$ Joules$6.4 \times 10^{8}$ Joules$6.4 \times 10^{9}$ JoulesCorrect Option: 1 Solution:...
Read More →A uniform string of length
Question: A uniform string of length $20 \mathrm{~m}$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is :(take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ ) $\sqrt{2} \mathrm{~s}$$2 \pi \sqrt{2} \mathrm{~s}$$2 s$$2 \sqrt{2} \mathrm{~s}$Correct Option: , 4 Solution:...
Read More →Two particles of equal mass
Question: Two particles of equal mass ' $m$ ' go around a circle of radius $\mathrm{R}$ under the action of their mutual gravitational attraction. The speed of each particle with respect to their centre of mass is:-$\sqrt{\frac{\mathrm{Gm}}{\mathrm{R}}}$$\sqrt{\frac{G m}{4 R}}$$\sqrt{\frac{\mathrm{Gm}}{3 \mathrm{R}}}$$\sqrt{\frac{\mathrm{Gm}}{2 \mathrm{R}}}$Correct Option: , 3 Solution:...
Read More →The above is a plot of binding energy per nucleon
Question: The above is a plot of binding energy per nucleon $\mathrm{E}_{\mathrm{b}}$, against the nuclear mass $\mathrm{M} ; \mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}, \mathrm{F}$ correspond to different nuclei. Consider four reactions: (i) $\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}+\varepsilon$ (ii) $\mathrm{C} \rightarrow \mathrm{A}+\mathrm{B}+\varepsilon$ (iii) $\mathrm{D}+\mathrm{E} \rightarrow \mathrm{F}+\varepsilon$ (iv) $\mathrm{F} \rightarrow \mathrm{D}+\mathrm{E}+\v...
Read More →Two charges each equal toq$ are kept at x=-a and x=a on the x-axis.
Question: Two charges each equal to $\mathrm{q}$ are kept at $\mathrm{x}=-\mathrm{a}$ and $\mathrm{x}=\mathrm{a}$ on the $\mathrm{x}$-axis. A particle of mass $\mathrm{m}$ and charge $\mathrm{q}_{0}=\frac{\mathrm{q}}{2}$ is placed at the origin. If charge $\mathrm{q}_{0}$ is given a small displacement $(\mathrm{y}\mathrm{a})$ along the $\mathrm{y}$-axis, the net force acting on the particle is proportional to y- y$\frac{1}{y}$$-\frac{1}{y}$Correct Option: 1 Solution:...
Read More →Two bodies of masses
Question: Two bodies of masses $\mathrm{m}$ and $4 \mathrm{~m}$ are placed at a distance $\mathrm{r}$. The gravitational potential at a point on the line joining them where the gravitational field is zero is :-$-\frac{6 \mathrm{Gm}}{\mathrm{r}}$$-\frac{9 \mathrm{Gm}}{\mathrm{r}}$zero$-\frac{4 \mathrm{Gm}}{\mathrm{r}}$Correct Option: , 2 Solution:...
Read More →A sonometer wire of length
Question: A sonometer wire of length $1.5 \mathrm{~m}$ is made of steel. The tension in it produces an elastic strain of $1 \%$. What is the fundamental frequency of steel if density and elasticity of steel are $7.7 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ and $2.2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$ respectively ? $188.5 \mathrm{~Hz}$$178.2 \mathrm{~Hz}$$200.5 \mathrm{~Hz}$$770 \mathrm{~Hz}$Correct Option: 2, Solution:...
Read More →The height at which
Question: The height at which the acceleration due to gravity becomes $\frac{\mathrm{g}}{9}$ (where $\mathrm{g}=$ the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is :-$\frac{R}{2}$$\sqrt{2} \mathrm{R}$$2 \mathrm{R}$$\frac{R}{\sqrt{2}}$Correct Option: , 3 Solution:...
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