Some Basic doubts in mechanics

for 4m, in x direction , F - N_x = 4ma_x

for m , in y direction , F + f - mg = ma_y
in x direction , N_x =ma_x
so F = 5ma_x
for a_y = 0
F +f = mg
F + μN_x = mg , i.e F + μF5 = mg
F = 5mg5+μ

for m₁ , m₂ to be stationary wrt M , a_x of all three shud be equal and a_y of m₂ = 0

now F - N - T = Ma
T = m₁a
N = m₂a

so , a = Fm₁+m₂+M

for m₂ , T + f = m₂g

T = m₁a = m₁ Fm₁+m₂+M

so m₁Fm₁+m₂+M + f = m₂g

μN = μm₂Fm₁+m₂+M
when f = +μN , F = minimum , when f = - μN i.e opp direction, F = max

so F_max = m₂g(m₁+m₂+M)m₁ - μm₂
F_min= m₂g(m₁+m₂+M)m₁ +μm₂

so (m₁+m₂+M)gm₁ m₂+μ≤ F ≤ (m₁+m₂+M)gm₁ m₂-μ

now just check wich option doesnt lie in dis range

aer first ka answer post karna bhul gaya [3]

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