A solid metal sphere of volume 2 m ^3 is placed in a pressure chamber and subjected to a uniform pressure of 4 10^7 N m ⁻² . If the bulk modulus of the metal is 8 10¹⁰ N m ⁻² , the absolute decrease in the volume of the sphere is cm ^3 .

Step-by-step solution

The bulk modulus B is given by the formula: B = P ( V V ) Rearranging to solve for the absolute decrease in volume V : V = P V B Substitute the given values: V = 4 10^7 2 8 10¹⁰ V = 8 10^7 8 10¹⁰ = 10⁻³ m ^3 To convert the volume change into cm ^3 , multiply by 10^6 (since 1 m ^3 = 10^6 cm ^3 ): V = 10⁻³ 10^6 cm ^3 = 1000 cm ^3 . Answer: 1000