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Question: Evaluate $\left|\begin{array}{cc}2 \cos \theta -2 \sin \theta \\ \sin \theta \cos \theta\end{array}\right|$ Solution:...
Read More →The surface tension of water is 72 dyne/cm.
Question: The surface tension of water is 72 dyne/cm. Convert it to SI 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 →The normal duration of I.Sc physics practical period
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...
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Question: Evaluate $\left|\begin{array}{cc}2 \cos \theta -2 \sin \theta \\ \sin \theta \cos \theta\end{array}\right|$. Solution:...
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 →The height of a mercury column in a barometer in a Calcutta
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 $=\mathrm{h \rho g}$ in usual symbols Solution: $\mathrm{H}=75 \mathrm{~cm}$, density of mercury $=13600 \mathrm{~kg} / \mathrm{m}^{3}, \mathrm{~g}=9.8 \math...
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Question: Evaluate $\left|\begin{array}{cc}\sqrt{6} \sqrt{5} \\ \sqrt{20} \sqrt{24}\end{array}\right|$ Solution:...
Read More →The average speed of a snail is
Question: The average speed of a snail is $0.020 \mathrm{miles} /$ hour and that of a leopard is $70 \mathrm{miles} / \mathrm{hour}$. 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 →Suppose the acceleration due to gravity at a place
Question: Suppose the acceleration due to gravity at a place is $10 \mathrm{~m} / \mathrm{s}^{2}$. Find its value in $\mathrm{cm} /(\text { minute })^{2}$. Solution: $\mathrm{g}=10 \mathrm{metre} / \mathrm{sec}^{2}=10 \times 100 \times 3600 \mathrm{~cm} / \mathrm{min}^{2} .=36 \times 10^{5} \mathrm{~cm} / \mathrm{min}^{2}$...
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Question: Evaluate $2\left|\begin{array}{cc}7 -2 \\ -10 5\end{array}\right|$ Solution:...
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Question: If $A=\left[\begin{array}{ll}3 4 \\ 1 2\end{array}\right]$, find the value of $3|A|$ Solution:...
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Question: If $\left|\begin{array}{cc}2 x x+3 \\ 2(x+1) x+1\end{array}\right|=\left|\begin{array}{cc}1 5 \\ 3 3\end{array}\right|$, write the value of $x$. Solution:...
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Question: If $\left|\begin{array}{cc}2 x 5 \\ 8 x\end{array}\right|=\left|\begin{array}{cc}6 -2 \\ 7 3\end{array}\right|$, write the value of $x$ Solution:...
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Question: If $\left|\begin{array}{cc}3 x 7 \\ -2 4\end{array}\right|=\left|\begin{array}{ll}8 7 \\ 6 4\end{array}\right|$, write the value of $x$ Solution:...
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Question: Evaluate $\left|\begin{array}{cc}a+i b c+i d \\ -c+i d a-i b\end{array}\right|$ Solution:...
Read More →Taking force,
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 $=\frac{\text { mass }}{\text { volume }}=\frac{\frac{\text { force }}{\text { accelearation }}}{\text { volume }}=\left[\mathrm{F} / \mathrm{LT}^{-2}\right]\left[\mathrm{L}^{3}\right]=\left[\mathrm{FL}-4 \mathrm{~T}^{-2}\right]$ (b) Pressure $=$ force/area $=[F] \backslash\left[L^{2}\right]=\left[\mathrm{FL}^{-2}\right]$ (c) Moment...
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Question: Evaluate $\left|\begin{array}{cc}x^{2}-x+1 x-1 \\ x+1 x+1\end{array}\right|$ Solution:...
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Question: If $A_{i j}$ is the cofactor of the element $a_{i j}$ of $\left|\begin{array}{ccc}2 -3 5 \\ 6 0 4 \\ 1 5 -7\end{array}\right|$ then write the value of $\left(a_{32} A_{32}\right)$. Solution:...
Read More →Find the dimensions of
Question: Find the dimensions of (a) the specific heat capacity c, (b) the coefficient of linear expansion a, (c) the gas constant $\mathrm{R}$ 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] /[\...
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Question: Let $A$ be a square matrix of order 3 , write the value of $|2 \mathrm{~A}|$, where $|\mathrm{A}|=4$. Solution:...
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Question: If $\mathrm{A}$ is a $3 \times 3$ matrix such that $|\mathrm{A}| \neq 0$ and $|3 \mathrm{~A}|=\mathrm{k}|\mathrm{A}|$ then write the value of $k$. Solution:...
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Question: If $A$ is a $2 \times 2$ matrix such that $|A| \neq 0$ and $|A|=5$, write the value of $|4 A|$. Solution:...
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 $=q \mathrm{~L}=[\mathrm{IT}] \times[\mathrm{L}]=[\mathrm{LIT}]$ (b) Magnetic dipole moment $=I A=[I] \times\left[L^{2}\right]=\left[I L^{2}\right]$...
Read More →Find the dimensions of
Question: Find the dimensions of (a) Electric field, (b) Magnetic field, (c) Magnetic permeability $\mu_{0}$ Solution: (a) Electric field $=\mathrm{F} / \mathrm{q}=\left[\mathrm{MLT}^{-2}\right] /[\mathrm{IT}]=\left[\mathrm{MLT}^{-3} \mathrm{~J}^{-1}\right]$ (b) Magnetic field $=\mathrm{F} / \mathrm{qv}=\left[\mathrm{MLT}^{-2}\right] /[\mathrm{IL}]=\left[\mathrm{MT}^{-2} \mathrm{I}^{-1}\right]$ (c) Magnetic Permeability $=\mathrm{B} \times 2 \pi \mathrm{a} / \mathrm{I}=\left[\mathrm{MT}^{-2} \ma...
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