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51.

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

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

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

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

$\frac{\mathrm{h}}{\mathrm{e}}$

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If C be the capacitance and V be the electric potential, then the dimensional formula of CV^{2} is

[ML

^{2}T^{-2}A^{0}][MLT

^{-2}A^{-1}][M

^{0}LT^{-2}A^{0}][ML

^{-3}TA]

A.

[ML^{2}T^{-2}A^{0}]

We know,

Energy, E = CV^{2}

Dimensions of CV^{2} = Dimensions of energy

= [ML^{2}T^{-2}]

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53.

The dimensional formula of physical quantity is is [M^{a}L^{b}T^{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

54.

Which one of the following is not correct ?

Dimensional formula of thermal conductivity (K) is M

^{1}L^{1}T^{-3}K^{-1}Dimensional formula of potential (V) is M

^{1}L^{2}T^{3}A^{-1}Dimensional formula of permeability of free space (μ

_{0}) is M^{1}L^{1}T^{-2}A^{-2}Dimensional formula of RC M

^{0}L^{0}T^{-1}

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55.

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 %

56.

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

angular momentum

time

velocity

frequency

57.

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

3.3

3300

3302

33.0

58.

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

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