Units and Measurement

The dimensions of resistance are same as those of where h is the Planck's constant, e is the charge.

• $\frac{{\mathrm{h}}^2}{{\mathrm{e}}^2}$

• $\frac{{\mathrm{h}}^2}{\mathrm{e}}$

• $\frac{\mathrm{h}}{{\mathrm{e}}^2}$

• $\frac{\mathrm{h}}{\mathrm{e}}$

If C be the capacitance and V be the electric potential, then the dimensional formula of CV² is

• [ML²T^-2A⁰]

• [MLT^-2A^-1]

• [M⁰LT^-2A⁰]

• [ML^-3TA]

The dimensional formula of physical quantity is is [M^aL^bT^c]. Then, that physical quantity is

• Spring constant if a = 1, b = −1, c = −2

• surface tension if a= 1, b = 1,c = −2

• force if a = 1, b = 1, c = 2

• angular frequency if a = 0, b = 0, c = − 1

Which one of the following is not correct ?

• Dimensional formula of thermal conductivity (K) is M¹L¹T^-3K^-1

• Dimensional formula of potential (V) is M¹L²T³A^-1

• Dimensional formula of permeability of free space (μ₀) is M¹L¹T^-2A^-2

• Dimensional formula of RC M⁰L⁰T^-1

A physical quantity Q is found to depend on observables x, y and z obeying relation $\mathrm{Q} = \frac{{\mathrm{x}}^3{\mathrm{y}}^2}{\mathrm{z}}$. The percentage error in the measurements of x, y and z are 1 %, 2 % and 4 % respectively. What is percentage error in the quantity Q ? 

• 4 %

• 3 %

• 11 %

• 1 %

The ratio of the dimensions of Planck's constant and that of moment of inertia has the dimensions of

• angular momentum

• time

• velocity

• frequency

A substance of mass 49.53 g occupies 1.5 cm³ of volume. The density of the substance (in g cm^-3) with correct number of significant figures is

• 3.3

• 3300

• 3302

• 33.0

A body of the mass 50 kg is suspended using a spring balance inside a lift at rest. If the lift starts falling freely, the reading of the spring balance is

• < 50 kg

• = 50 kg

• > 50 kg

• = 0

The S.I. unit of specific heat capacity is

• JK^-1

• J kg^-1

• J mol^-1 K^-1

• J kg^-1 K^-1