If \(E\) and \(G\) respectively, denote energy and gravitational constant, then \(\dfrac{E}{G}\) has the dimensions of:
1. \([ML^0T^0]\)
2. \([M^2L^{-2}T^{-1}]\)
3. \([M^2L^{-1}T^{0}]\)
4. \([ML^{-1}T^{-1}]\)

A screw gauge gives the following readings when used to measure the diameter of a wire:
Main scale reading: \(0\) mm
Circular scale reading: \(52\) divisions 
Given that \(1\) mm on the main scale corresponds to \(100\) divisions on the circular scale, the diameter of the wire that can be inferred from the given data is:

If force \([F]\), acceleration \([A]\) and time \([T]\) are chosen as the fundamental physical quantities, then find the dimensions of energy:
1. \(\left[FAT^{-1}\right]\)
2. \(\left[FA^{-1}T\right]\)
3. \(\left[FAT\right]\)
4. \(\left[FAT^{2}\right]\)

\(5.74\) g of a substance occupies \(1.2~\text{cm}^3\). Its density by keeping the significant figures in view is:
1. \(4.7333~\text{g/cm}^3\)
2. \(3.8~\text{g/cm}^3\)
3. \(4.8~\text{g/cm}^3\)
4. \(3.7833~\text{g/cm}^3\)

We measure the period of oscillation of a simple pendulum. In successive measurements, the readings turn out to be \(2.63~\text s, 2.56~\text s, 2.42~\text s, 2.71~\text s,\) and \(2.80~\text s.\) The average absolute error and percentage error, respectively, are:
1. \(0.22~\text s\) and \(4\%\)
2. \(0.11~\text s\) and \(4\%\)
3. \(4~\text s\) and \(0.11\%\)
4. \(5~\text s\) and \(0.22\%\)

The dimensions of \((\mu_0\varepsilon_0)^{\frac{-1}{2}}\) are:
1. \(\left[L^{-1}T\right]\)
2. \(\left[LT^{-1}\right]\)
3. \(\left[L^{{-1/2}}T^{{1/2}}\right]\)
4. \(\left[L^{{-1/2}}T^{{-1/2}}\right]\)

The radius of a circle is stated as \(2.12\) cm. Its area should be written as:

The dimensions of ${\left({\mu }_0{\epsilon }_0\right)}^{-1/2}$ are:

1.  $[$ $L^{-1}T$ $]$

2.  $[$ $L{T}^{-1}$ $]$

3.  $[$ $L^{1/2}{T}^{1/2}$ $]$

4. $[$ $L^{1/2}{T}^{-1/2}$ $]$

Time intervals measured by a clock give the following readings: 
\(1.25~\text{s},~1.24~\text{s}, ~1.27~\text{s},~1.21~\text{s},~1.28~\text{s}.\) 
What is the percentage relative error of the observations? 
1. \(2\)%
2. \(4\)%
3. \(16\)%
4. \(1.6\)%