AP EAPCET 07-Jul-2022 Shift 2 Paper

As, block has a tendency to slide downwards, friction acts in upward direction.
Box will not slide if friction balances component of weight acting in downward direction.
⇒f≥mg‌sin‌θ ...(i)
Here, f= friction =µN
or f=µ[(mg‌cos‌θ)+F] ...(ii)
As, applied force is perpendicular to surface of incline.
Normal reaction, N= net perpendicular to surface force
=mg‌cos‌θ+F
Hence, by Eqs.(i) and (ii) we have
µ(mg‌cos‌θ)+µF≥mg‌sin‌θ
or F≥

mg‌sin‌θ−µmg‌cos‌θ

µ

...(iii)
here, m=2‌kg
g=10m∕ s2
sin‌θ=sin‌30∘=

1

2

µ=0.2
So, F≥(

2×10× 1 2 −0.2×2×10× √3 2

0.2

)
⇒F≥50−17.32
⇒F≥3267
or F≥327
Hence, minimum value of F is 32.7N