Why is my answer for the rotating wedge problem not matching?

[Prabs3257]

Homework Statement

A wedge is fixed on a moving Square Plate with angular velocity w = √(g/l) and side of the plate is l then the coefficient of friction between the block and the wedge such that there is no relative motion ?? assuming that side of plate is very large as compared to width and height of the wedge

Relevant Equations

Fc = mv^2/r

I tried making the fbd of both blocks the block on the incline will have mgsin30 friction force, tension and centrepetal force's cos component similarly second block will have mg tension and friction where normal will be centrepetal force after solving my ans is not matching

 

[haruspex]

the block on the incline will have mgsin30 friction force,

I assume you mean that will be its normal force, but you are forgetting the rotation.
Please post an fbd for that block.

 

[Prabs3257]

I assume you mean that will be its normal force, but you are forgetting the rotation.
Please post an fbd for that block.

for the block on incline i got the quation umg√3/2 + mg/2 = T + mw²l√3/2

and for the other block mg = T + umw²l

by solving these two equation i got the value of u but that's not matching please tell me where i am wrong

 

[haruspex]

umg√3/2

As I wrote, this is wrong.
What is the equation for the normal force on the block?

 

[Prabs3257]

As I wrote, this is wrong.
What is the equation for the normal force on the block?

Is the normal not mgcos30 ??

 

[Prabs3257]

Is the normal not mgcos30 ??

Ohhhhh i got it centrifugal force will also affect the normal

 

[Prabs3257]

As I wrote, this is wrong.
What is the equation for the normal force on the block?

Thanks i corrected my mistake and got the correct ans

 

[haruspex]

Thanks i corrected my mistake and got the correct ans

Well done.