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Chapter 1: Problem 109
Which of the following numerical value have significant figure \(4 ?\) (a) \(1.011\) (b) \(0.010\) (c) \(0.001\) (d) \(0.100\)
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Match column - I with column - II $$ \begin{array}{|l|l|} \hline \multicolumn{1}{|c|} {\text { Column - I }} & \multicolumn{1}{|c|} {\text { Column - II }} \\ \hline \text { (1) capacitance } & \text { (a) } \mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-3} \mathrm{~A}^{-1} \\ \hline \text { (2) Electricfield } & \text { (b) } \mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-1} \\ \hline \text { (3) planck's constant } & \text { (c) } \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{~A}^{2} \\ \hline \text { (4) Angular momentum } & \text { (d) } \mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-1} \\ \hline \end{array} $$ (a) \(a, c, b, d\) (b) \(c, a, d, b\) (c) \(c, a, b, d\) (d) \(a, b, d, c\)
Dimensions of impulse are. (a) \(\mathrm{M}^{-1} \mathrm{~L}^{-1} \mathrm{~T}^{1}\) (b) $\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-1}$ (c) \(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{1}\) (d) \(\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-2}\)
Pressure \(P=\left(a t^{2} / b x\right)\) where \(x=\) distance, \(t=\) time find the dimensional formula for \(\mathrm{a} / \mathrm{b}\) (a) \(\mathrm{M}^{1} \mathrm{~L}^{0} \mathrm{~T}^{-4}\) (b) \(\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-1}\) (c) \(\mathrm{M}^{1} \mathrm{~L}^{0} \mathrm{~T}^{-2}\) (d) \(\mathrm{M}^{+1} \mathrm{~L}^{0} \mathrm{~T}^{-2}\)
The periodic time of simple pendulum is $\mathrm{T}=2 \pi \sqrt{(\ell / \mathrm{g})}\( relative error in the measurement of \)\mathrm{T}\( and \)\ell$ are \(\pm \mathrm{a}\) and \(\pm \mathrm{b}\) respectively find relative error in the measurement of \(g\) (a) \(a+b\) (b) \(2 \mathrm{~b}+\mathrm{a}\) (c) \(2 \mathrm{a}+\mathrm{b}\) (d) \(a-b\)
Dimensional formula for power is (a) \(\mathrm{M}^{2} \mathrm{~L}^{-2} \mathrm{~T}^{-3}\) (b) \(\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-2}\) (c) \(\mathrm{M}^{1} \mathrm{~L}^{3} \mathrm{~T}^{-1}\) (d) \(\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-2}\)
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