If C and L denote the capacitance and inductance, the dimensions of LC are
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Solution
From v=\(\frac{1}{2\pi \sqrt{LC}}\)
LC=\(\frac{1}{(2\pi v)^{2}}=\frac{1}{(T^{-1})^{2}}=T^{2}=[M^{0}L^{0}T^{2}]\)
What is the unit of “a” in Vander Waal’s gas equation?
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Solution
The vander Waal’s gas equation is
\(\left ( p+\frac{a}{V^{2}} \right )(v-b)=RT\) for one mole.
& \(\left ( P+\frac{\mu a}{V^{2}} \right )(V-\mu b)=\mu RT\) for μ mole.
Dimensionally in first bracket on L.H.S
[P]=\(\left [ \frac{\mu a}{V^{2}} \right ]\Rightarrow [a]=\frac{[p]V^{2}}{\mu }\)
Dimension of [a]=\(\left [ \frac{atm.litre^{2}}{mole} \right ]\)
Temperature can be expressed as derived quantity in terms of
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Solution
Temperature is one of the basic physical quantities.
The least count of a stopwatch is 0.2 second. The time of 20oscillations of a pendulum is measured to be 25 second.The percentage error in the measurement of time will be
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Solution
\(\frac{0.2}{25}\times 100=0.8\)
The dimensional formula of current density is
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Solution
Current density=\(\frac{Current}{area}=\frac{Q}{area\times t}\)
If L and R denote inductance and resistance then dimension of L/R is
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Solution
L/R=\(\frac{Volt\times sec/amp.}{Volt/amp.}\)= sec=[M0L0T0]
Let Q denote the charge on the plate of a capacitor of capacitance C. The dimensional formula for \(\frac{Q^{2}}{C}\) is
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Solution
We know that \(\frac{Q^{2}}{2C}\) is energy of capacitor so it represent the dimension of energy [ML2T-2].
Area of a square is (100 ± 2) m2. Its side is
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Solution
Area = (Length)2
or length=(Area)1/2
=(100 ± 2)1/2
=(100)1/2±1⁄2×2
=(100 ± 1)m
Relative density of a metal may be found with the help of spring balance. In air the spring balance reads (5.00 ± 0.05) N and in water it reads (4.00 ± 0.05) N. Relative density would be
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Solution
Relative density =\(\frac{Weight\, of\, body\, in\, air}{Loss\, of\, weight\, in\, water}\)
\(\frac{5.00}{5.00–4.00}=\frac{5.00}{1.00}\)
\(\frac{\Delta \rho }{\rho }\times 100=\left ( \frac{0.05}{5.00}+\frac{0.05}{1.00} \right )\times 100\)
= (0.01 +0.05) × 100
= 0.06 × 100 = 6%
∴Relative density =5.00±6%
When 97.52 is divided by 2.54, the correct result is
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Solution
\(\frac{97.52}{2.54}\)=38.393=38.4(with least number of significant figures,3).