Figure shows three blocks on a rough surface under the influene of a force `P` of the same magnitude in all the three cases. Coefficient of friction is the same between each block and the ground. What possile relation holds between the magnitudes of normal reaction and friction force?(Assume that the blocks do not overturn about edge.) Here `f_(A), f_(B)` and `f_(C)` are frictional forces and `N_(A), N_(B)` and `N_(C)` are reactions.

Options

A. `N_(A)gtN_(C)gtN_(B)`
B. `f_(A)gtf_(C)gtf_(B)`
C. `f_(C)gtf_(A)=f_(B)`
D. `N_(C)gtN_(A)=N_(B)`

Answer

A, B, D

Explanation

`N_A=mg+"P"sintheta`
`N_B=mg-"P"sintheta`
`N_C=mg`
Clearly, `N_AgtN_CgtN_B`
Now to find relation between frictions:
i. Let sliding not occur:
`f_A=Pcostheta, f_B=Pcostheta, f_C=P`
`implies f_Cgtf_A=f_B`
ii. Let sliding occur of all contact surfaces:
`f_A=muN_A, f_B=muN_B, f_C=muN_C`
`implies f_Agtf_Cgtf_B`