If A represents density, B represents velocity, C represents specific heat capacity and D represents wavelength, then the quantity having the dimensions of product of A, B, C and D is

Question

If A represents density, B represents velocity, C represents specific heat capacity and D represents wavelength, then the quantity having the dimensions of product of A, B, C and D is (A) Stefan's constant (B) Boltzmann's constant (C) thermal conductivity (D) universal gas constant

Tardigrade Admin · Accepted Answer

According to the question, Given, A= density, B= velocity, C= specific heat capacity and D= wavelength So, dimensions of A, B, C and D are A=[M L-3 T0] B=[M0 L T-1], C=[M0 L2 T-2 K-1] and D=[ M 0 L T 0] Hence, dimension of A B C D= [ ML -3 T 0][ M 0 L T -1][ M 0 L 2 T -2 K -1][ M 0 LT 0] =[ ML (-3+1+2+1) T (-1-2) K -1]=[ MLT -3 K -1] or A B C D=[ MLT -3 K -1] ldots(i) Now, dimension of each given option, (a) Stefan's constant =[ ML 0 T -3 K -4] (b) Boltzmann's constant =[ ML 2 T 2 K -1] (c) Thermal conductivity =[ MLT -3 K -1] (d) Universal gas constant =[ ML 2 T -2 K -1] So, the dimension of product of A, B, C and D is same as dimension of thermal conductivity.

Q. If A represents density, B represents velocity, C represents specific heat capacity and D represents wavelength, then the quantity having the dimensions of product of A,B,C and D is

Stefan's constant

Boltzmann's constant

thermal conductivity

universal gas constant

Q. If $A$ represents density, $B$ represents velocity, $C$ represents specific heat capacity and $D$ represents wavelength, then the quantity having the dimensions of product of $A, B, C$ and $D$ is