1.A standard 1 kilogram weight is a cylinder 41.5 mm in height and 51.0 mm in diameter. What is the density of the material? (answer unit: kg/m^3) *2.A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a crystal as shown in Figure a. The atoms reside at the corners of cubes of side L = 0.160 nm. One piece of evidence for the regular arrangement of atoms comes from the flat surfaces along which a crystal separates, or cleaves, when it is broken. Suppose this crystal cleaves along a face diagonal, as shown in Figure b. Calculate the spacing d between two adjacent atomic planes that separate when the crystal cleaves. (answer unit: nm) *3.Assume the equation x = At3 + Bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. Determine the dimensions of the constants A and B. (Use the following as necessary: L and T, where L is the unit of length and T is the unit of time.) [A] = *4.Assume the equation x = At3 + Bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. Determine the dimensions of the constants A and B. (Use the following as necessary: L and T, where L is the unit of length and T is the unit of time.) [B] = *5.Determine the dimensions of the derivative dx/dt = 3At2 + B. (Use the following as necessary: L and T, where L is the unit of length and T is the unit of time.) [dx/dt] = *