NEET Questions

A protein molecule's diameter is measured as 42 Å using X-ray diffraction. If another measurement instrument gives the diameter in picometers (pm), and the ratio of the two measurements is $\frac{x}{10}$, what is the value of $x$?

The ionization energy of hydrogen is 13.6 eV. Express this energy in joules per mole using the following conversions: 1 eV = $1.602 imes 10^{-19}$ J and Avogadro's number = $6.022 imes 10^{23}$ $mol^{-1}$.

The density of a substance is given as 0.8 g/$cm^3$. Convert this density to kg/$m^3$.

The Planck constant is $6.626 imes 10^{-34}$ J s. Express this in units of eV s (electron-volt seconds), given 1 eV = $1.602 imes 10^{-19}$ J.

The time period of a simple pendulum is given by $T = 2\pi\sqrt{\frac{l}{g}} + kx$, where $l$ is the length, $g$ is acceleration due to gravity, and $x$ is displacement. The dimensions of $k$ are:

If the velocity (v), acceleration (a), and time (t) are chosen as fundamental quantities, the dimensional formula for force is:

The dimensions of coefficient of viscosity are:

The period $T$ of oscillation of a spring-mass system depends on the mass $m$ and the spring constant $k$. Using dimensional analysis and the principle of homogeneity, determine the relationship between $T$, $m$, and $k$.

The viscous force $F$ acting on a sphere moving through a liquid depends on the radius $r$ of the sphere, the velocity $v$ of the sphere, and the coefficient of viscosity $η$ of the liquid. If $F = kη^arv^b$, where $k$ is a dimensionless constant, using dimensional analysis, find the values of $a$, $b$.

The viscous force $F$ acting on a sphere of radius $r$ moving with velocity $v$ through a fluid of viscosity $\eta$ is given by $F = 6\pi \eta rv$. If a new physical quantity $Q$ is defined as $Q = \frac{Fv^2}{\eta^2 r^3}$, the dimensions of $Q$ are: