The density of material in CGS system of units is 4 ~g / cm ^3 . In a system of units in which unit of lengths is 10 ~cm and unit of mass is 100 ~g , the value of density of material will be

Step-by-step solution

Mass, aligned & M=d V & d= M L^3 & d=4 ~g / cm ^3 aligned If unit of mass is 100 ~g and unit of distance is 10 ~cm . So, density aligned y & = 4 ( 100 ~g 100 ) ( 10 10 ~cm )^3 & = ( 4 100 ) ( 1 10 )^3 (100 ~g ) (10 ~cm )^3 & =40 ~g ~cm ⁻³ aligned Aliter aligned u₂ & =u₁ ( M₁ M₂ ) ( L₁ L₂ )⁻³ & =4 ( 1 100 ) ( 1 10 )⁻³ & =40 aligned