The velocity of a particle (v) at an instant t is given by $$v = at + b{t^2}$$ the dimension of b is
A quantity $X$ is given by $\varepsilon_0 L \frac{\Delta V}{\Delta t}$, where $\varepsilon_0$ is the permittivity of free space, $L$ is the length, $\Delta V$ is a potential difference and $\Delta t$ is a time interval. The dimension of $X$ is same as that of
The resistance $\mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}}$ where $\mathrm{V}=(25 \pm 0.4)$ Volt and $\mathrm{I}=(200 \pm 3)$ Ampere. The percentage error in ' $R$ ' is
The Power $$(\mathrm{P})$$ radiated from an accelerated charged particle is given by $$\mathrm{P} \propto \frac{(q \mathrm{a})^{\mathrm{m}}}{\mathrm{c}^{\mathrm{n}}}$$ where $$\mathrm{q}$$ is the charge, $$\mathrm{a}$$ is the acceleration of the particle and $$\mathrm{c}$$ is speed of light in vacuum. From dimensional analysis, the value of $$m$$ and $$n$$ respectively, are
Which of the following quantity has the dimension of length ?
(h is Planck's constant, m is the mass of electron and c is the velocity of light)
In an experiment, the length of an object is measured to be 6.50 cm. This measured value can be written as 0.0650 m. The number of significant figures on 0.0650 m is
A modified gravitational potential is given by $$\mathrm{V}=-\frac{\mathrm{GM}}{\mathrm{r}}+\frac{\mathrm{A}}{\mathrm{r}^{2}}$$. If the constant A is expressed in terms of gravitational constant (G), mass (M) and velocity of light (c), then from dimensional analysis, A is,
Given : The percentage error in the measurements of A, B, C and D are respectively, 4%, 2%, 3% and 1%. The relative error in $$Z = {{{A^4}{B^{{1 \over 3}}}} \over {C{D^{{3 \over 2}}}}}$$ is
The Entropy (S) of a black hole can be written as $$S = \beta {k_B}A$$, where kB is the Boltzmann constant and A is the area of the black hole. The $$\beta$$ has dimension of