TS EAMCET 9 May 2024 Shift 2 Solved Paper

Let the body slide a distance s along the incline before coming to rest.
So, it ascends by a vertical height h=ssin‌θFrom work-energy theorem,
‌∆Wff+∆Wmg=∆KE
⇒‌‌−µmg(cos‌θ)s−mgssin‌θ=0−E
⇒‌‌µmgs‌cos‌θ+mgssin‌θ=E
⇒‌‌s=‌

E

mg(µ‌cos‌θ+sin‌θ)

So work done by friction,
∆Wff=−µmgs‌cos‌θ=‌

−µE‌cos‌θ

µ‌cos‌θ+sin‌θ

-ve sign is for direction.