A solid Hemisphere rests in equilibrium on a rough ground and against a smooth wall. The curved surface touches the wall and the ground. The angle of inclination of the circular base to the horizontal is 30°, If minimum coefficient of friction required between ground and hemisphere is μ. Find value of 32 μ.

Question

A solid Hemisphere rests in equilibrium on a rough ground and against a smooth wall. The curved surface touches the wall and the ground. The angle of inclination of the circular base to the horizontal is 30°, If minimum coefficient of friction required between ground and hemisphere is μ. Find value of 32 μ. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f = mg × (3 R /8) cos 60° N 2= f N 1= mg f =(3 mg /16) f ≤ μ N 1 μ ≥ (3/16) ⇒ 32 μ=6

f=mg×83R​cos60∘ N2​=f N1​=mg f=163mg​ f≤μN1​ μ≥163​ ⇒32μ=6

$f = m g \times \frac{3 R}{8} cos 6 0^{\circ}$
$N_{2} = f$
$N_{1} = m g$
$f = \frac{3 m g}{16}$
$f \leq μ N_{1}$
$μ \geq \frac{3}{16}$
$\Rightarrow 32 μ = 6$