Guess a relation among the quantities using the method of dimensions.
Question: Theory of relativity reveals that mass can be converted into energy. The energy $E$ so obtained is proportional to certain powers of mass $m$ and the speed of light c. Guess a relation among the quantities using the method of dimensions. Solution: Let us assume energy $E \alpha m^{a} c^{b}$, or $E=k m^{a} c^{b}$, where $k$ is a constant Equating their dimensions $\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]=\left[\mathrm{M}^{\mathrm{a}}\right]\left[\mathrm{L}^{\mathrm{b}} \mathrm{T}^{...
Read More →Moment of inertia of a sphere about its diameter is
Question: The kinetic energy $\mathrm{K}$ of a rotating body depends on its moment of Inertia I and its angular speed $\omega$. Assuming the relation to be $\mathrm{K}=\mathrm{kl}^{\mathrm{a}} \omega^{\mathrm{b}}$, where $\mathrm{k}$ is a dimensionless constant, find $\mathrm{a}$ and $\mathrm{b}$. Moment of inertia of a sphere about its diameter is $\frac{2}{5} M r^{2}$ Solution: $\mathrm{K}=\mathrm{kl}^{\mathrm{a}} \mathrm{\omega}^{\mathrm{b}}$, where $\mathrm{k}=$ constant and $\mathrm{K}=$ Ki...
Read More →The surface tension of water is 72 dyne/cm. Convert it to Sl unit.
Question: The surface tension of water is 72 dyne/cm. Convert it to Sl unit. Solution: Surface tension of water is $72 \mathrm{dyne} / \mathrm{cm}$ In S.I. unit, it is $=0.072 \mathrm{~N} / \mathrm{m}$...
Read More →Express this period in microcenturies.
Question: The normal duration of I.Sc physics practical period in Indian colleges is 100 minutes. Express this period in microcenturies. 1 microcentury $=10^{-6} \times 100$ years. Solution: 1 microcentury $=10-4$ years. $=10-4 \times 365 \times 24 \times 60 \mathrm{~min}=52.56 \mathrm{~min}$. So, 100 min $=100 / 52.26$ microcentury $=1.9$ microcentury...
Read More →Express the power of a 100 watt bulb in CGS unit
Question: Express the power of a 100 watt bulb in CGS unit Solution: 1 watt $=1$ Joule $/ \mathrm{sec}=10^{7} \mathrm{erg} / \mathrm{sec}$ So, 100 watt $=10^{9} \mathrm{erg} / \mathrm{sec}$....
Read More →Calculate this pressure in SI and CGS
Question: The height of a mercury column in a barometer in a Calcutta Laboratory was recorded to be $75 \mathrm{~cm}$. Calculate this pressure in SI and CGS using the following data: Specific gravity of mercury $=13.6$, Density of water $=1000 \mathrm{~kg} / \mathrm{m}^{3}, \mathrm{~g}=9.8 \mathrm{~m} / \mathrm{s}^{2}$ at Calcutta. Pressure $=\mathrm{h} \rho \mathrm{g}$ in usual symbols Solution: $\mathrm{H}=75 \mathrm{~cm}$, density of mercury $=13600 \mathrm{~kg} / \mathrm{m}^{3}, \mathrm{~g}=...
Read More →Convert these speeds in SI units.
Question: The average speed of a snail is $0.020$ miles/hour and that of a leopard is $70 m i l e s /$ hour. Convert these speeds in SI units. Solution: 1 mile $=1.6 \mathrm{~km}=1600 \mathrm{~m}$, and 1 hour $=3600$ seconds. Speed of snail $=0.02 \times 1600 / 3600$ metre per sec $=0.0089 \mathrm{~m} / \mathrm{sec}$. Speed of leopard $=70 \times 1600 / 3600$ metre per sec $=31 \mathrm{~m} / \mathrm{sec}$....
Read More →Taking force, length and time to be fundamental quantities find the dimensions of
Question: Taking force, length and time to be fundamental quantities find the dimensions of a)Density, b)Pressure, c) momentum and d)energy Solution: a) Density $=\frac{\text { mass }}{\text { volume }}=\frac{\frac{\text { jurcelenration }}{\text { volume }}}{\text { volum }}=\left[\mathrm{F} / \mathrm{LT}^{-2}\right]\left[\mathrm{L}^{3}\right]=\left[\mathrm{FL}^{-4} \mathrm{~T}^{-2}\right]$ b) Pressure $=\frac{\text { force/area }}{\text { force }}=[\mathrm{F}]\left[\mathrm{L}^{2}\right]=\left[...
Read More →Find the dimensions
Question: Find the dimensions of a)the specific heat capacity $c$ b)the coefficient of linear expansion a, c) the gas constant R Solution: a) Specific heat constant $c=Q / m\left(T_{2}-T_{1}\right)=\left[M^{2} T^{-2}\right] /[M][\theta]=\left[L^{2} T^{-2} \theta^{-1}\right]$ b) Coefficient of linear expansion $\alpha=\frac{[L]}{[L][\theta]}=[\theta]$ c) Gas constant $=\mathrm{R}=\mathrm{PV} / \mathrm{nT}=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]\left[\mathrm{L}^{3}\right][\mathrm{mol}][\the...
Read More →Find the dimensions of Planck's constant h
Question: Find the dimensions of Planck's constant $h$ from the equation $E=h v$ where $E$ is energy and $v$ is frequency Solution: $h=\frac{E}{v}$ So, $[\mathrm{h}]=\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right] /\left[\mathrm{T}^{-1}\right]=\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]$...
Read More →Find the dimensions of
Question: Find the dimensions of a) Electric dipole moment p, b) magnetic dipole moment M Solution: a) Electric dipole moment $=\mathrm{qL}=[\mathrm{IT}] \times[\mathrm{L}]=[\mathrm{LIT}]$ b) Magnetic dipole moment $=I A=[I] \times\left[L^{2}\right]=\left[I^{2}\right]$...
Read More →Find the dimensions of
Question: Find the dimensions of a)Electric field, b)Magnetic field, c)Magnetic permeability 0 Solution: a)Electric field $=F / q=\left[\mathrm{MLT}^{-2}\right] /[\mathrm{IT}]=\left[\mathrm{ML}^{-3} \mathrm{~T}^{-1}\right]$ b) Magnetic field $=\mathrm{F} / \mathrm{qv}=\left[\mathrm{ML} \mathrm{T}^{-2}\right] /[\mathrm{L}]=\left[\mathrm{MT}^{-2} \mathrm{|}^{-1}\right]$ c) Magnetic Permeability $=\mathrm{B} \times 2 \pi \mathrm{\pi a} / \mathrm{l}=\left[\mathrm{MT}^{-2} \mathrm{~F}^{-1}\right][\ma...
Read More →Find the dimensions of
Question: Find the dimensions of a)angular speed, b) angular acceleration, c) Torque T c)moment of Inertia I Solution: a) Angular speed $=$ radian/time $=\left[\mathrm{M}^{0} \mathrm{O}^{-1}\right]$ b) Angular acceleration $=$ Angular speed/time $=\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{-2}\right]$ c) Torque $=\vec{r} \times \vec{F}=\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]$ d) Moment of Inertia $=\mathrm{Mr}^{2}=\left[\mathrm{ML}^{2}\right]$...
Read More →Find the dimensions of
Question: Find the dimensions of a) linear momentum b) frequency c) pressure Solution: a) Linear momentum = mv Dimension $=\left[\mathrm{MLT}^{-1}\right]$ b) Frequency $=1 / T$ Dimension $=\left[\mathrm{T}^{-1}\right]$ c) Pressure = Force/Area Dimension $=\left[\mathrm{MLT}^{-2}\right] /\left[\mathrm{L}^{2}\right]=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]$...
Read More →Match the catalysts (Column I) with products (Column II).
Question: Match the catalysts (Column I) with products (Column II). (A)-(ii); (B)-(iii); (C)-(i); (D)-(iv)(A)-(iii); (B)-(i); (C)-(ii); (D)-(iv)(A)-(iii); (B)-(iv); (C)-(i); (D)-(ii)(A)-(iv); (B)-(iii); (C)-(ii); (D)-(i)Correct Option: , 2 Solution:...
Read More →The mojor product of the following reaction is :
Question: The mojor product of the following reaction is : $\mathrm{CH}_{3} \mathrm{CD}(\mathrm{Cl}) \mathrm{CHD}$ (I)$\mathrm{CH}_{3} \mathrm{CD}_{2} \mathrm{CH}(\mathrm{Cl})$ (I)$\mathrm{CH}_{3} \mathrm{CD}(\mathrm{I}) \mathrm{CHD}(\mathrm{Cl})$$\mathrm{CH}_{3} \mathrm{C}(\mathrm{I})(\mathrm{Cl}) \mathrm{CHD}_{2}$Correct Option: , 4 Solution:...
Read More →For any given series of spectral lines of atomic hydrogen,
Question: For any given series of spectral lines of atomic hydrogen, let $\Delta \bar{v}=\bar{v}_{\max }-\bar{v}_{\min }$ be the difference in maximum and minimum frequencies in $\mathrm{cm}^{-1}$. The ratio $\Delta \bar{v}_{\text {Lyman }} / \Delta \bar{v}_{\text {Balmer }}$ is :$27: 5$$4: 1$$5: 4$$9: 4$Correct Option: , 4 Solution:...
Read More →Solve this following
Question: At $300 \mathrm{~K}$ and 1 atmospheric pressure, $10 \mathrm{~mL}$ of a hydrocarbon required $55 \mathrm{~mL}$ of $\mathrm{O}_{2}$ for complete combustion and $40 \mathrm{~mL}$ of $\mathrm{CO}_{2}$ is formed. The formula of the hydrocarbon is:$\mathrm{C}_{4} \mathrm{H}_{8}$$\mathrm{C}_{4} \mathrm{H}_{7} \mathrm{Cl}$$\mathrm{C}_{4} \mathrm{H}_{10}$$\mathrm{C}_{4} \mathrm{H}_{6}$Correct Option: , 4 Solution:...
Read More →The element having greatest difference between
Question: The element having greatest difference between its first and second ionization energies, is :$\mathrm{Ca}$$\mathrm{K}$$\mathrm{Ba}$$\mathrm{Sc}$Correct Option: , 2 Solution:...
Read More →Which of the following is a condensation polymer?
Question: Which of the following is a condensation polymer?Buna $-\mathrm{S}$Nylon 6,6TeflonNeopreneCorrect Option: , 2 Solution: Nylon-6,6 is a condensation polymer of hexamethylene diamine and adipic acid. Buna-S, Teflon and Neoprene are addition polymer....
Read More →Aniline dissolved in dilute
Question: Aniline dissolved in dilute $\mathrm{HCl}$ is reacted with sodium nitrite at $0^{\circ} \mathrm{C}$. This solution was added dropwise to a solution containing equimolar mixture of aniline and phenol in dil. HCl. The structure of the major product is :Correct Option: 1 Solution:...
Read More →Liquid 'M' and liquid 'N' form an ideal solution.
Question: Liquid 'M' and liquid 'N' form an ideal solution. The vapour pressures of pure liquids 'M' and ' $\mathrm{N}$ ' are 450 and $700 \mathrm{mmHg}$, respectively, at the same temperature. Then correct statement is: $\left(x_{\mathrm{M}}=\right.$ Mole fraction of 'M' in solution ; $x_{\mathrm{N}}=$ Mole fraction of 'N' in solution ; $y_{\mathrm{M}}=$ Mole fraction of 'M' in vapour phase ; $y_{\mathrm{N}}=$ Mole fraction of ' $\mathrm{N}$ ' in vapour phase)$\left(x_{\mathrm{M}}-y_{\mathrm{M}...
Read More →Magnisium powder burns in air to give:
Question: Magnisium powder burns in air to give:$\mathrm{MgO}$ only$\mathrm{MgO}$ and $\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}$$\mathrm{MgO}$ and $\mathrm{Mg}_{3} \mathrm{~N}_{2}$$\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}$ and $\mathrm{Mg}_{3} \mathrm{~N}_{2}$Correct Option: , 3 Solution: $\mathrm{Mg}+\underset{\mathrm{O}_{2} / \mathrm{N}_{2}}{\operatorname{air} \stackrel{\Delta}{\longrightarrow}} \mathrm{MgO}+\mathrm{Mg}_{3} \mathrm{~N}_{2}$...
Read More →Consider the statements S1 and S2 :
Question: Consider the statements S1 and S2 : S1 : Conductivity always increases with decrease in the concentration of electrolyte. S2 : Molar conductivity always incrteases with decrease in the concentration of electrolyte. The correct option among the following is :Both $\mathrm{S} 1$ and $\mathrm{S} 2$ are correct$\mathrm{S} 1$ is wrong and $\mathrm{S} 2$ is correct$\mathrm{S} 1$ is correct and $\mathrm{S} 2$ is wrongBoth $\mathrm{S} 1$ and $\mathrm{S} 2$ are wrongCorrect Option: , 2 Solution...
Read More →The major product of the following
Question: The major product of the following reaction is : $\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CHCO}_{2} \mathrm{CH}_{3} \stackrel{\mathrm{LiAlH}_{4}}{\longrightarrow}$$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CHO}$$\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CHCH}_{2} \mathrm{OH}$$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CO}_{2} \mathrm{CH}_{3}$$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}$Correct Option: , 2 Solution:...
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