Q.

A  very  large  plank  P  of  some  unknown  mass  is  being  moved with a constant velocity  v0i^ 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 v0k^ . All  these  velocities  are  with  respect  to  ground frame  and  at  t  =  0.  Coefficient  of  friction  between  the plank and the block is μ .  Choose the CORRECT option(s).

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a

At t = 0, power developed (with respect to ground frame) by kinetic friction force on the block B is μmg2v0

b

Kinetic friction force acting on the block, at t = 0 is  μmgk^

c

At t = 0, heat dissipation per sec in the system is 2μmgv0

d

At t = 0, power developed (with respect to ground frame) by kinetic friction force on the block μmgv02

answer is B, D.

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Detailed Solution

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From frame of reference of P , velocity of block is vnet=-v0i^+v0k^

So, kinetic friction acts exactly in opposite direction of vnet.

Magnitude of fk is μmg but to express in vector form, we have to take its components.

fk on the block B=μmg(12i^12k^)​Option (A) is incorrect.​Now, from ground frame, power is​Pfk=μmg[i^2k^2](v0k^)Pfk=μmgv02To find heat dissipation we have to observe from plank frame​dQdt=μmg[i^2k^2](v0i^+v0k^)=μmgv022=2μmgv0​Negative sign indicates dissipation.

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A  very  large  plank  P  of  some  unknown  mass  is  being  moved with a constant velocity  v0i^ 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 v0k^ . All  these  velocities  are  with  respect  to  ground frame  and  at  t  =  0.  Coefficient  of  friction  between  the plank and the block is μ .  Choose the CORRECT option(s).