Units & Measurement and Dimensions

Match the physical quantities given in List-I with dimensions expressed in terms of mass (M), length (L), time (T) and electric current (A) given in List-II.List-IList-II(a) Torque(i) $[M^{-1}L^{-2}T^{4}A^{2}]$(b) Gravitational constant(ii)...

Which of the following expression can be deduced on the basis of dimensional analysis? (All symbols have their usual meanings)

Dimensional formula for activity of a radioactive substance is

The true length of a wire is \(3.678 \mathrm{~cm}\). When the length of this wire is measured using instrument \(A\), the length of the wire is \(3.5 \mathrm{~cm}\). When the length of the wire is measured using instrument \(B\), it is foun...

The Vernier scale of a travelling microscope has 50 divisions which coincides with 49 main scale divisions. If each main scale division is \(0.5 \mathrm{~mm}\), then the least count of the microscope is

A cylindrical wire has a mass \((0.3 \pm 0.003) \mathrm{g}\), radius \((0.5 \pm 0.005) \mathrm{mm}\) and length \((6 \pm 0.06) \mathrm{cm}\). The maximum percentage error in the measurement of its density is

If \(P, Q\) and \(R\) are physical quantities having different dimensions, which of the following combinations can never be a meaningful quantity?

The dimensions of the ratio of magnetic flux
$(\phi)$ and permeability $(\mu)$ are

A substance of mass 49.53 g occupies $1.5 \mathrm{~cm}^3$ of volume. The density of the substance (in $\mathrm{g} \mathrm{cm}^{-3}$ ) with correct number of significant figures is