Which one of the following represents the correct dimensions of the coefficient of viscosity?
ML^{−1} T^{−2}
MLT^{−1}
ML^{−1} T^{−1}
ML^{−1} T^{−1}
When the voltage and current in a conductor are measured as (100 ± 4) V and (5 ± 0.2) A, then the percentage of error in the calculation of resistance is
8 %
4 %
20 %
10 %
The set of physical quantities among the following which are dimensionally different is
terminal velocity, drift velocity, critical velocity
potential energy, work done, kinetic energy
dipole moment, electric flux, electric field
distintegration constant, frequency, angular velocity
The physical quantity that does not have the dimensional formula [ML^{-1}T^{-2}] is
force
pressure
stress
modulus of elasticity
A dorce F is applied onto a square plate of side L. If the percentage error in determining L is 2 % and that in F is 4 %, the permissible percentage error in determining the pressure is
2 %
4 %
6 %
8 %
In a simple pendulum experiment, the maximum percentage error in the measurement of length is 2% and that in the observation of the time-period is 3%. Then, the maximum percentage error in determination of the acceleration due to gravity g is
5 %
6 %
7 %
8 %
D.
8 %
The maximum percentage error
$\frac{\u2206\mathrm{g}}{\mathrm{g}}=\frac{\u2206\mathrm{l}}{\mathrm{l}}+{\left|\frac{\u2206\mathrm{T}}{\mathrm{T}}\right|}^{2}\phantom{\rule{0ex}{0ex}}=\frac{{\displaystyle \u2206\mathrm{l}}}{{\displaystyle \mathrm{l}}}+2\frac{\u2206\mathrm{T}}{\mathrm{T}}\mathrm{where}\frac{{\displaystyle \u2206\mathrm{l}}}{{\displaystyle \mathrm{l}}}=2\%\phantom{\rule{0ex}{0ex}}\frac{{\displaystyle \u2206\mathrm{g}}}{{\displaystyle \mathrm{g}}}=2\%+2\times 3\%\phantom{\rule{0ex}{0ex}}=2\%+6\%\phantom{\rule{0ex}{0ex}}=8\%$
The pitch and the number of circular scale divisions in a screw gauge with least count 0.02 mm are respectively
1 mm and 100
0.5 mm and 50
1 mm and 50
0.5 mm and 100
The quantity which has the same dimensions as that of gravitational potential is
latent heat
impulse
angular acceleration
Planck's constant
The percentage error in measuring M, L and T are 1 %, 1.5% and 3% respectively. Then the percentage error in measuring the physical quantity with dimensions [ML^{-1 }T^{-1}] is
1 %
3.5 %
5.5 %
4.5 %
The displacement of a particle moving along x-axis with respect to time t is x = at + bt^{2} − ct^{3}. The dimensions of c are
[T^{-3}]
[LT^{-2}]
[LT^{-3}]
[LT^{3}]