Question Bank Directory

If dimensions of critical velocity $v_c$ of a liquid flowing through a tube are expressed as $[\eta^x \rho^y r^z]$, where $\eta$, $\rho$ and $r$ are the coefficient of viscosity of the liquid, the density of liquid and radius of the tube respectively, then the values of $x$, $y$ and $z$ are given by

Dimensional formula $ML^2T^{-3}$ represents

The dimension of $\frac{1}{2}\varepsilon_0 E^2$, where $\varepsilon_0$ is permittivity of free space and $E$ is electric field, is

The density of material in the CGS system of units is $4\text{ g/cm}^3$. In a system of units in which unit of length is $10\text{ cm}$ and unit of mass is $100\text{ g}$, the value of density of material in this system will be:

If force $[F]$, acceleration $[A]$ and time $[T]$ are chosen as the fundamental physical quantities, then find the dimensions of energy:

A force defined by $F = \alpha t^2 + \beta t$ acts on a particle at a given time $t$. The factor which is dimensionless, if $\alpha$ and $\beta$ are constants, is:

The percentage errors in the measurement of mass and momentum of an object are 1% and 2% respectively. The percentage error in the measurement of kinetic energy of the object will be:

The area of a rectangular field (in $\text{m}^2$) of length $55.3$ m and breadth $25$ m after rounding off the value, for correct significant digits is:

When the circular scale of a screw gauge completes 2 rotations, it covers 1 mm over the pitch scale. The total number of circular scale divisions is 50. The least count of the screw gauge in metres is:

The mechanical quantity, which has dimensions of reciprocal of mass ($M^{-1}$), is:

A metal wire has mass $(0.4\pm 0.002)\text{ g}$, radius $(0.3\pm 0.001)\text{ mm}$ and length $(5\pm 0.02)\text{ cm}$. The maximum possible percentage error in the measurement of density will nearly be:

The intermediate compound 'X' in the following chemical reaction is: $$\text{Toluene} \xrightarrow{CrO_2Cl_2/CS_2} X \xrightarrow{H_3O^+} \text{Benzaldehyde}$$

If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{E}{G}$ has the dimensions of:

Uncertainty in position of an electron ($e^-$) and Helium atom (He) is similar. If uncertainty in momentum of electron is $32 \times 10^5$, then uncertainty in momentum of Helium will be:

The radius of a hydrogen shell is 0.53 Å. In its first excited state, radius of the shell will be:

The product(s) formed from the following reaction is/are:

For a p-type semiconductor, which of the following statements is true ?

The unit of thermal conductivity is :

Which one is the wrong statement?

Drug called 'Heroin' is synthesized by