Question

A block of mass $m$ starts sliding on the plank of mass $M$. There is a sufficient friction between plank and the block. After some time both block and plank moves together. Choose the correct statement

• A. Total mechanical energy of system constant
• B. The kinetic energy of system increases
• C. The total mechanical energy of system decreases
• D. The linear momentum of system is not conserve

Answer 1

The correct option is C

The total mechanical energy of system decreases

Using the law of conservation of energy, the system only had kinetic energy possessed by mass m initially. As it started sliding, friction started acting in it, then obviously some amount of initial energy will be dissipated in form of heat energy. The rest of the remaining energy is in the form of kinetic energy of both the blocks combined. But this kinetic energy is less than the initial kinetic energy of block of mass $m$. If $K_m$ is the initial kinetic of block $m$ and $E_f$ is the amount of energy dissipated due to friction and $K_{M+m}$ is the kinetic energy of composite block, then it can be said that

$K_m=E_f+K_{M+m}$