A body is moving up an inclined plane of angle θ with an initial kinetic energy E. The coefficient of friction between the plane and the body is μ. The work done against friction before the body comes to rest is
μE cos θμ cos θ+sin θ
Let the body slide a distance s along the incline before coming to rest. So, it ascends by a vertical height h=s sin θ.
From the work-energy theorem, ΔWfr+ΔWmg=ΔK⇒−μmg (cos θ) s−mgs sin θ=0−E⇒μmgs cos θ+mgs sin θ=E⇒s=Emg(μ cos θ+sin θ)
So, the work done by friction, ΔWfr=−μmgs cos θ=−μ Ecos θμ cos θ+sin θ
Hence, the work done against friction is μE cos θμ cos θ+sin θ and the correct choice is (d).