The Young's modulus of a steel wire of length 6 m and cross-sectional area 3 mm 2 , is 2 × 11 11 N / m 2 . The wire is suspended from its support on a given planet. A block of mass 4 kg is attached to the free end of the wire. The acceleration due to gravity on the planet is 1 4 of its value on the earth. The elongation of wire is (Take g on the earth = 10 m / s 2 ):

Step-by-step solution

The external force or tension F acting on the wire is its own weight. It is given by F =   m g = 4   kg × 10 4   m   s - 2 = 10   N The formula to calculate the Young's modulus of the material of the wire is given by Y =   F A ∆ L L =   F L ∆ L A . . . . . . . . . . . . . . . . . . . . . . . . . . ( 1 ) where, A is the cross-sectional area, L is the original length and ∆ L is the elongation of the wire. Substitute the given values of the known parameters