A small slider of mass m is released from rest while in position A and then slides along the vertical-plane track. The track is smooth from A to D and rough (coefficient of kinetic friction μk=(1/√3) ) from point D onwards. The distance s traveled along the incline past point D before the slider stops is n R. Find n.

Question

A small slider of mass m is released from rest while in position A and then slides along the vertical-plane track. The track is smooth from A to D and rough (coefficient of kinetic friction μk=(1/√3) ) from point D onwards. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/0a72136e3e214ef13dbac3bfc09782b0-.png" /> The distance s traveled along the incline past point D before the slider stops is n R. Find n. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

(1/2) m vD2=m g(d sin 30°)+(μ m g cos 30°) d ∵ vD=vB ⇒ d=2 R

21​mvD2​=mg(dsin30∘)+(μmgcos30∘)d ∵vD​=vB​ ⇒d=2R

$\frac{1}{2} m v_{D}^{2} = m g (d sin 3 0^{\circ}) + (μ m g cos 3 0^{\circ}) d$
$∵ v_{D} = v_{B}$
$\Rightarrow d = 2 R$