A very large plank `P` of some unknown mass is being moved with velocity `v_(0)hati` under application of an external force (not shown in figure). Simultaneously a block `B` of mass `m` placed on the plank is also moving with velocity `v_(0)hatk`. All these velocities are with respect to ground frame and at `t=0`. Coefficient of frictioin between the plank and the block `mu`. Choose the correct option(s).

Options

A. Kinetic friction force acting on the block at `t=0` is `-mumghatk`
B. At `t=0`, power developed (with respect to ground frame) by kinetic friction force on the block `B` is `-(mu mg v_(0))/(sqrt(2))`
C. At `t=0` power developed (with respect to ground frame) by kinetic friction force on the block `B` is `-mu mg sqrt(2) v_(0)`
D. At `t=0`, heat dissipation per sec in the system is `2sqrt(2)mu mg v_(0)`

Answer

B, C

Explanation

`vecf_(k)` on the block `B=mu mg(1/(sqrt(2)) hati-1/(sqrt(2))hatk)`
`P_(f_(k))=mu mg [(hati)/(sqrt(2))-(hatk)/(sqrt(2))].(v_(0)hatk)`
`=-(mu mg v_(0))/(sqrt(2))`
`(dQ)/(dt)=mumgv_(0)2/(sqrt(2))=sqrt(2) mu mg v_(0)`