The potential energy of a point particle is given by the expression $V(x)=-\alpha x+\beta \sin (x / \gamma)$. A dimensionless combination of the constants $\alpha, \beta$ and $\gamma$ is
If $L,\,C$ and $R$ represent inductance, capacitance and resistance respectively, then which of the following does not represent dimensions of frequency
The speed of a wave produced in water is given by $v=\lambda^a g^b \rho^c$. Where $\lambda$, g and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $a , b$ and $c$ respectively, are
The equation $\frac{{dV}}{{dt}} = At - BV$ is describing the rate of change of velocity of a body falling from rest in a resisting medium. The dimensions of $A$ and $B$ are
A spherical body of mass $m$ and radius $r$ is allowed to fall in a medium of viscosity $\eta $. The time in which the velocity of the body increases from zero to $0.63$ times the terminal velocity $(v)$ is called time constant $(\tau )$. Dimensionally $\tau $ can be represented by