The dimensions of $K$ in the equation $W = \frac{1}{2}\,\,K{x^2}$ is

  • A

    ${M^1}{L^0}{T^{ - 2}}$

  • B

    ${M^0}{L^1}{T^{ - 1}}$

  • C

    ${M^1}{L^1}{T^{ - 2}}$

  • D

    ${M^1}{L^0}{T^{ - 1}}$

Similar Questions

In the relation : $\frac{d y}{d x}=2 \omega \sin \left(\omega t+\phi_0\right)$ the dimensional formula for $\left(\omega t+\phi_0\right)$ is :

A system has basic dimensions as density $[D]$, velocity $[V]$ and area $[A]$. The dimensional representation of force in this system is 

If the units of force, energy and velocity are respectively $10\, N, 100\, J, 5\, m/s$, then  the units of length, mass and time will be

Young-Laplace law states that the excess pressure inside a soap bubble of radius $R$ is given by $\Delta P=4 \sigma / R$, where $\sigma$ is the coefficient of surface tension of the soap. The EOTVOS number $E_0$ is a dimensionless number that is used to describe the shape of bubbles rising through a surrounding fluid. It is a combination of $g$, the acceleration due to gravity $\rho$ the density of the surrounding fluid $\sigma$ and a characteristic length scale $L$ which could be the radius of the bubble. A possible expression for $E_0$ is 

  • [KVPY 2013]

The time dependence of a physical quantity $P$ is given by $ P = P_0 exp^{(-\alpha t^{2})} $ where $\alpha$ is a constant and $t$ is time. The constant $\alpha$ 

  • [AIPMT 1993]