A student measured the diameter of a small steel ball using a screw gauge of least count \(0.001\) cm. The main scale reading is \(5\) mm and zero of circular scale division coincides with \(25\) divisions above the reference level. If the screw gauge has a zero error of \(-0.004\) cm, the correct diameter of the ball is:
1. | \(0.521\) cm | 2. | \(0.525\) cm |
3. | \(0.053\) cm | 4. | \(0.529\) cm |
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. \([FvT^{-1}]\)
2. \([FvT^{-2}]\)
3. \([Fv^{-1}T^{-1}]\)
4. \([Fv^{-1}T]\)
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. | \(a=1,\) \(b=-1,\) \(c=-2\) | pressure if
2. | \(a=1,\) \(b=0,\) \(c=-1\) | velocity if
3. | \(a=1,\) \(b=1,\) \(c=-2\) | acceleration if
4. | \(a=0,\) \(b=-1,\) \(c=-2\) | force if
If the error in the measurement of the radius of a sphere is 2%, then the error in the determination of the volume of the sphere will be:
1. 4%
2. 6%
3. 8%
4. 2%
Which two of the following five physical parameters have the same dimensions?
(1) | Energy density |
(2) | Refractive index |
(3) | Dielectric constant |
(4) | Young's modulus |
(5) | Magnetic field |
Choose the correct option:
1. | (2) and (4) |
2. | (3) and (5) |
3. | (1) and (4) |
4. | (1) and (5) |