If dimensions of critical velocity \({v_c}\) of a liquid flowing through a tube are expressed as \(\eta^{x}\rho^yr^{z}\), where \(\eta, \rho~\text{and}~r\) are the coefficient of viscosity of the liquid, the density of the liquid, and the radius of the tube respectively, then the values of \({x},\) \({y},\) and \({z},\) respectively, will be:
1. \(1,-1,-1\)
2. \(-1,-1,1\)
3. \(-1,-1,-1\)
4. \(1,1,1\)
1. | \([Ev^{-2}T^{-1}]\) | 2. | \([Ev^{-1}T^{-2}]\) |
3. | \([Ev^{-2}T^{-2}]\) | 4. | \([E^{-2}v^{-1}T^{-3}]\) |
If force (\(F\)), velocity (\(\mathrm{v}\)), and time (\(T\)) are taken as fundamental units, the dimensions of mass will be:
1. \( {\left[\mathrm{FvT}^{-1}\right]} \)
2. \({\left[\mathrm{FvT}^{-2}\right]} \)
3. \( {\left[\mathrm{Fv}^{-1} \mathrm{~T}^{-1}\right]} \)
4. \( {\left[\mathrm{Fv}^{-1} \mathrm{~T}\right]}\)
The dimensions of where is the permittivity of free space and E is the electric field, are:
1. [ML2T-2]
2. [ML-1T-2]
3. [ML2T-1]
4. [MLT-1]
1. | pressure if \(a=1,\) \(b=-1,\) \(c=-2\) |
2. | velocity if \(a=1,\) \(b=0,\) \(c=-1\) |
3. | acceleration if \(a=1,\) \(b=1,\) \(c=-2\) |
4. | force if \(a=0,\) \(b=-1,\) \(c=-2\) |
Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, length L, time T, and current I, would be:
1.
2.
3.
4.
The velocity \(v\) of a particle at time \(t\) is given by \(v=at+\frac{b}{t+c}\), where \(a,\) \(b\) and \(c\) are constants. The dimensions of \(a,\) \(b\) and \(c\) are respectively:
1. | \(\left[\mathrm{LT}^{-2}\right],[\mathrm{L}] \text { and }[\mathrm{T}]\) |
2. | \( {\left[\mathrm{L}^2\right],[\mathrm{T}] \text { and }\left[\mathrm{LT}^2\right]} \) |
3. | \( {\left[\mathrm{LT}^2\right],[\mathrm{LT}] \text { and }[\mathrm{L}]} \) |
4. | \( {[\mathrm{L}],[\mathrm{LT}] \text { and }\left[\mathrm{T}^2\right]}\) |
The unit of thermal conductivity is:
1. | W m–1 K–1 | 2. | J m K–1 |
3. | J m–1 K–1 | 4. | W m K–1 |