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The position of a particle at time $t$ is given by the relation $l = \frac{v_0}{\alpha}(1 - e^{\alpha t})$, where $v_0$ is a constant and $\alpha > 0$. The dimensions of $v_0$ and $\alpha$ are respectively
A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is : ($\alpha_{Cu} = 1.7 \times 10^{-5}$ K$^{-1}$ and $\alpha_{Al} = 2.2 \times 10^{-5}$ K$^{-1}$)
From dimensional considerations, which of the following equations is correct?
Whose dimensions are $ML^2T^{-1}$?
A physical quantity of the dimensions of length that can be formed out of $c$, $G$ and $\frac{e^2}{4\pi\varepsilon_0}$ is [$c$ is the velocity of light, $G$ is the universal constant of gravitation and $e$ is charge]
Which of the following system of units is not based on units of mass, length and time alone?
If force ($F$), velocity ($v$) and time ($T$) are taken as fundamental units, then the dimensions of mass are
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:
If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{E}{G}$ has the dimensions of:
For a p-type semiconductor, which of the following statements is true ?