AP EAPCET (DEMO) PHYSICS UNITS & DIMENSIONS PAPER

The dimensions of universal gravitational constant are

If $$v=A/t+B t^{2}+C t^{3}$$ where $$v$$ is velocity, $$t$$ is time and $$A, B$$ and $$C$$ are constants, then the dimensional formula of $$B$$ is

The frequency of vibration $$f$$ of a mass $$m$$ suspended from a spring of spring constant $$k$$ is given by relation of the type $$f=c m^{x} k^{y}$$, where $$c$$ is dimensionless constant. The values of $$x$$ and $$y$$ are

If $$E=$$ energy, $$G=$$ gravitational constant, $$I=$$ impulse and $$M=$$ mass, the dimensions of $$\frac{G I M^{2}}{E^{2}}$$ are same as that of

Frequency is the function of density $$(\rho)$$, length $$(a)$$ and surface tension $$(T)$$. Then its value is

In the relation $$p=\frac{\alpha}{\beta}{e}^{\frac{-\alpha z}{k \theta}} $$ P is the pressure, $$z$$ the distance, $$k$$ is Boltzmann constant and $$\theta$$ is the temperature, the dimensional formula of $$\beta$$ will be

The position of a particle at time $$t$$ is given by the relation , where $$v_{0}$$ is constant and $$\alpha>0$$. The dimensions of $$v_{0}$$ and $$\alpha$$ are respectively

The dimensional formula of relative density is

Consider a new system of units in which $$c$$ (speed of light in vacuum), $$h$$ (Planck’s constant) and $$G$$ (gravitational constant) are taken as fundamental units. Which of the following would correctly represent mass in this new system?

The equation of a wave is given by
$$Y=A \sin \omega(\frac{x}{v}-k)$$
where $$\omega$$ is the angular velocity and $$v$$ is the linear velocity.
The dimension of $$k$$ is

The dimensions of permittivity $$\varepsilon_{0}$$ are

The speed $$(v)$$ of ripples on the surface of water depends on surface tension $$(\sigma)$$, density $$(\rho)$$ and wavelength $$(\lambda)$$. The square of speed $$(v)$$ is proportional to

If $$C$$ and $$R$$ represent capacitance and resistance respectively, then the dimensions of $$R C$$ are

If $$L$$ and $$R$$ are respectively the inductance and resistance, then the dimensions of $$\frac{L}{R}$$ will be

If energy $$(E)$$, velocity $$(v)$$ and force $$(F)$$ be taken as fundamental quantity, then what are the dimensions of mass