Final answer:
The energy transferred to the second block is represented by the expression (1/2 m v²), which indicates the kinetic energy of the first block just before the collision.
Step-by-step explanation:
The expression that would give the energy transferred to the second block when a block of mass (m) is slid down a rough inclined plane and runs into another 1 kg block, coming to rest, is (1/2 m v²). This is because the kinetic energy of the first block just before the collision is all transferred to the second block at the moment the first block comes to rest. The kinetic energy is given by (1/2 m v²), where m is the mass of the sliding block and v is its velocity just before impact.