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Find out min. value of P to start the motion.

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There are two possibilities. One is that block A moves over block B and the other is that both blocks move together over the ground.

Case 1 : Let block A move over block B

$ ∴Σ F_x (→ +ve)=0 \\ ∴P \cos30-0.3 N_1 =0…………(I) \\ ∴Σ F_y (↑ +ve)=0 \\ ∴P \sin30+ N_1-100=0…………(II) $

Solving equations (I) and (II) simultaneously,

$P = 29.53 N ,N_1=85.24N $

Case 2: Let, both blocks move together over ground

$∴Σ F_x (→ +ve)=0 \\ ∴P \cos30-0.1 N_2=0…………(I) \\ ∴Σ F_y (↑ +ve)=0 \\ ∴P \sin30+ N_2=250…………(II) $

Solving equations (I) and (II) simultaneously,

$P = 27.29 N$

Minimum value of $P = 27.29N$ in which case both blocks will move together over the ground.

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