The dimension of ${\int }_u^{v}mvdv$ is

(1) $\left[M^1{L}^{-2}{T}^{-2}\right]$

(2) $\left[M^1{L}^2{T}^{-2}\right]$

(3) $\left[M^1{L}^1{T}^{-1}\right]$

(4) None of these

A screw gauge has the least count of \(0.01~\text{mm}\) and there are \(50\) divisions in its circular scale. The pitch of the screw gauge is:

The energy required to break one bond in DNA is \(10^{-20}~\text{J}\). This value in eV is nearly: 
1. \(0.6\)
2. \(0.06\)
3. \(0.006\)
4. \(6\)

Dimensions of stress are:

The dimensions of pressure are the same as that of

(1) Energy

(2) Energy per unit area

(3) Force per unit area

(4) Force per unit volume

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

A calorie is a unit of heat (energy in transit) and it equals about \(4.2~\text{J}\) where \(1~\text{J}= 1~\text{kg-m}^2\text{s}^{-2}\). Suppose we employ a system of units in which the unit of mass equals \(\alpha~\text{kg}\) the unit of length equals \(\beta~\text{m}\), and the unit of time is \(\gamma~\text{s}\) then the magnitude of calories in terms of new units is:
1. \(4.2\alpha^{-2}\beta^{-2}\gamma^{2}\)
2. \(4.2\alpha^{2}\beta^{-2}\gamma^{2}\)
3. \(4.2\alpha^{-1}\beta^{-2}\gamma^{2}\)
4. \(4.2\alpha^{-1}\beta^{2}\gamma^{-2}\)

The number of significant figures in \(0.0006032~\text m^2\) is: