A small ring R of mass 0.2 kg is threaded onto a fixed rod which is inclined at an angle of 30° to the horizontal. The ring is attached to a block B of mass 0.5 kg by means of a light string which pas

Question

A small ring R of mass 0.2 kg is threaded onto a fixed rod which is inclined at an angle of 30° to the horizontal. The ring is attached to a block B of mass 0.5 kg by means of a light string which passes over a smooth pulley P. The part RP of the string is perpendicular to the rod, and the part PB of the string is vertical (see diagram). The system is in equilibrium. Assuming the equilibrium is limiting, if the coefficient of friction ( $μ$ ) between R and the rod is $μ = \frac{1}{α - β}$ where $α$ and $β$ are the smallest possible integer. Fill the value of $(α + β)$ .

Answer:

8

Solution:

String tension $T = m_{B} g = 5$ N (equilibrium of B).

Normal on the ring: $N + T sin 3 0^{\circ} \cdot ... = N + 3 = 5$ N... friction $f = μ N$ balances the remaining component: $1 = μ (5 - 3)$ .

$μ = \frac{1}{5 - 3}$ , so $α = 5$ , $β = 3$

$α + β = 8$

TestHub · Accepted Answer

String tension T = m B ​ g = 5 N (equilibrium of B). Normal on the ring: N + T sin 3 0 ∘ ⋅ ... = N + 3 ​ = 5 N... friction f = μ N balances the remaining component: 1 = μ ( 5 − 3 ​ ) . μ = 5 − 3 ​ 1 ​ , so α = 5 , β = 3 α + β = 8

Physics - NLM Question with Solution | TestHub

Doubts & Discussion