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A very large plank P of some unknown mas...

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).

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)`

Text Solution

Verified by Experts

The correct Answer is:
B, C
`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)`
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