Units and Dimensions

Match List I with List II List I List II A Angular momentum I $\left[\mathrm{ML}^{2}T^{-2}\right]$ B Torque II $\left[\mathrm{ML}^{-2}T^{-2}\right]$ C Stress III $\left[\mathrm{ML}^{2}T^{-1}\right]$ D Pressure gradient…

A ball of radius $r$ and density $\rho$ dropped through a viscous liquid of density $\sigma$ and viscosity $\eta$ attains its terminal velocity at time $t$, given by $t=A \rho^{a} r^{b} \eta^{\mathrm{c}} \sigma^{d}$,…

Match List I with List II. List I List II (A) Torque (I) $\mathrm{Nms}^{-1}$ (B) Stress (II) $\mathrm{Jkg}^{-1}$ (C) Latent Heat (III) $\mathrm{Nm}$ (D) Power (IV) $\mathrm{Nm}^{-2}$ Choose the correct answer from the…

Match List I with List II List I List II A Torque I $\mathrm{kg}m^{-1}s^{-2}$ B Energy density II $\mathrm{kg}ms^{-1}$ C Pressure gradient III $\mathrm{kg}m^{-2}s^{-2}$ D Impulse IV $\mathrm{kg}m^{2}s^{-2}$ Choose the…

In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $\left[M^a L^b T^c\right]$. If $b=-3$, the value of $c$ is ________

Match List I with List II List I List II $A.$ Planck's constant $\left(h\right)$ $I.$ $\left[M^{1}L^{2}T^{-2}\right]$ $B.$ Stopping potential $\left(V_{s}\right)$ $\mathrm{II}.$ $\left[M^{1}L^{1}T^{-1}\right]$ $C.$ Work…

In the equation$\left[X+\frac{a}{Y^{2}}\right][Y-b]=RT,X$ispressure, $Y$is volume, $R$ is universal gas constant and$T$ is temperature. The physical quantity equivalentto the ratio$\frac{a}{b}$is:

Match List - I with List - II.List - IList - IIA. Boltzmann constantI. $[M^{-1}L^3T^{-2}]$B. Stefan's constantII. $[ML^2T^{-1}]$C. Planck's constantIII. $[ML^2T^{-2}K^{-1}]$D. Gravitational constantIV.…

Match List-I with List-II. List-IList-IIA. Meter (L)I. $\sqrt{\dfrac{hc}{G}}$B. Second (S)II. $\sqrt{\dfrac{Gh}{c^5}}$C. Kilogram (M)III. $\sqrt{\dfrac{K^2L^2c^3}{Gh}}$D. Kelvin (K)IV. $\sqrt{\dfrac{Gh}{c^3}}$ where $h$…

Match List I with List II List I List II A. Torque I. $ML^{-2}T^{-2}$ B. Stress II. $ML^{2}T^{-2}$ C. Pressure gradient III. $ML^{-1}T^{-1}$ D. Coefficient of viscosity IV. $ML^{-1}T^{-2}$ Choose the correct answer from…

Match List I with List II List-I List-II A Spring constant I $[T^{-1}]$ B Angular speed II $[MT^{-2}]$ C Angular momentum III $[ML^{2}]$ D Moment of Inertia IV $[ML^{2}T^{-1}]$ Choose the correct answer from the options…

Match List I with List II List List II A Young's Modulus $(Y)$ I $[\mathrm{ML}^{-1}T^{-1}]$ B Co-efficient of Viscosity $(\eta\,)$ II $[\mathrm{ML}^{2}T^{-1}]$ C Planck's Constant $(h)$ III $[\mathrm{ML}^{-1}T^{-2}]$ D…