If time T, acceleration A and force F are regarded as base units, then the dimensional formula of work is
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Solution
[A]=[LT-2] or [L]=[AT2]
[Work] = [Force × Distance] = [FL][FAT2]
The dimensional formula of farad is
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Solution
[C]=\(\left [ \frac{Q}{V} \right ]=\left [ \frac{Q^{2}}{W} \right ]=[M^{-1}L^{-2}T^{2}Q^{2}]\)
Given that r = m2 sin πt , where t represents time. If the unit of m is N, then the unit of r is
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Solution
Trigonometric ratio area number and hence demensionless
If I is the moment of inertia and ω the angular velocity,,what is the dimensional formula of rotational kinetic energy 1⁄2Iω2?
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Solution
Dimensionally K.E = Work
Specific gravity has ………… dimensions in mass, …………dimensions in length and ………… dimensions in time.
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Solution
Specific gravity is the ratio of density of substance and density of water at 4°C. The ratio of like quantities is dimensionless.
he speed of sound in a gas is given by v=\(\sqrt{\frac{\gamma RT}{M}}\)
R = universal gas constant,
T = temperature
M = molar mass of gas The dimensional formula of γ is
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Solution
Ratio of specific heat,γ= \(\frac{C_{p}}{C_{v}}\)
The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are 4% and 3% respectively,the maximum error in the measurement of density will be
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Solution
Density =\(\frac{Mass}{Volume}\)
ρ=\(\frac{M}{L^{3}}\),\(\frac{\Delta \rho }{\rho }=\frac{\Delta m}{m}+3\frac{\Delta L}{L}\)
% error in density = % error in Mass + 3 (% error in length)= 4 + 3(3) = 13%
The percentage errors in the measurement of mass and speed are 2% and 3% respectively. The error, in kinetic energy obtained by measuring mass and speed, will be
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Solution
Percentage error in mass\(\left ( \frac{\Delta m}{m}\times 100 \right )\)=2% and percentage error in speed \(\left ( \frac{\Delta V}{V}\times 100 \right )\)=3%
E=1⁄2mv2
∴\(\frac{\Delta E}{E}\times 100=\frac{\Delta m}{m}\times 100+2\frac{\Delta V}{V}\times 100\)
=2% + 2 × 3% =8%.
Using mass (M), length(L), time (T) and electric current (A)as fundamental quantities the dimensions of permittivity will be
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Solution
Force, F=\(\frac{1}{4\pi \varepsilon _{0}}\frac{q_{1}q_{2}}{r^{2}}\Rightarrow \varepsilon _{0}=\frac{q_{1}q_{2}}{4\pi Fr^{2}}\)
So dimension of ε0
\(=\frac{[AT]^{2}}{[MLT^{-2}][L^{2}]}=[M^{-1}L^{-3}T^{4}A^{2}]\)
A resistor of 10 k Ω having tolerance 10% is connected in series with another resistor of 20 k Ω having tolerance 20%.The tolerance of the combination will be
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Solution
Effective resistance
Rs(10kΩ±10%)+(20kΩ±20%)
∴ Tolerance of the combination= (30kΩ±30%)