If a rod of length , very small area of cross-section A, Young’s modulus of elasticity Y is acted upon by two parallel forces 3F and F respectively (as shown) and placed on a smooth horizontal plane. If the elastic limit is not crossed and then to study the change in length of rod Δ l and it’s elastic potential energy (U) the rod is segmented into four equal parts where magnitude of change in lengths are Δ l 1 , Δ l 2 , Δ l 3 , Δ l 4 and elastic potential energy stored in each segment are U 1 , U 2 , U 3 , U 4 respectively as shown then which is/are correct?

A cubical solid aluminium (bulk modulus = − V dP dV = 70 GPa) block has an edge length of 1 m on the surface of the earth. It is kept on the floor of a 5 km deep ocean. Taking the average density of water and the acceleration due to gravity to be 10 3 kg m −3 and 10 ms −2 , respectively, the change in the edge length of the block in mm is .

A composite rod consists of a steel rod of length 25 cm and area 2A and a copper rod of length 50 cm and area A. The composite rod is subjected to an axial load F. If the Young’s moduli of steel and copper are in the ratio 2:1, then

A ring of radius r made of wire of density ρ is rotated about a stationary vertical axis passing through its centre and perpendicular to the plane of the ring as shown in the figure. Determine the angular velocity (in rad/s) of ring at which the ring breaks. The Wire breaks at tensile stress σ . Ignore gravity. Take σ / ρ = 4 and r = 1 m.

A metal wire length L, cross-sectional area A and Young’s modulus Y is stretched by a variable force F. F is varying in such a way that F is always slightly greater than the elastic forces of resistance in the wire. When the elongation in the wire is l, up to this instant