Two bodies of masses m and 4 m are attached to a light string as shown in the figure. A body of mass m hanging from string is executing oscillations with angular amplitude 60°, while other body is at rest on a horizontal surface. The minimum coefficient of friction between mass 4 m and the horizontal surface is (here pulley is light and smooth)

Question

Two bodies of masses m and 4 m are attached to a light string as shown in the figure. A body of mass m hanging from string is executing oscillations with angular amplitude 60°, while other body is at rest on a horizontal surface. The minimum coefficient of friction between mass 4 m and the horizontal surface is (here pulley is light and smooth) (A) (1/4) (B) (3/4) (C) (1/2) (D) (1/8)

Tardigrade Admin · Accepted Answer

Velocity at lowest position, v=√2 g l(1- cos 60°.=√g l T=m g+(m v2/l)=m g+(m/l) g l=2 m g ∴ T =μ 4 m g ⇒ μ=(1/2)

$\frac{1}{4}$

$\frac{3}{4}$

$\frac{1}{2}$

$\frac{1}{8}$

Velocity at lowest position,
$v = 2 g l (1 - cos 6 0^{\circ} = g l$
$T = m g + \frac{m v ^{2}}{l} = m g + \frac{m}{l} g l = 2 m g$
$∴ T = μ 4 m g$
$\Rightarrow μ = \frac{1}{2}$

41​

43​

21​

81​

Velocity at lowest position, v=2gl(1−cos60∘​=gl​ T=mg+lmv2​=mg+lm​gl=2mg ∴T=μ4mg ⇒μ=21​

$\frac{1}{4}$

$\frac{3}{4}$

$\frac{1}{2}$

$\frac{1}{8}$

Velocity at lowest position,
$v = 2 g l (1 - cos 6 0^{\circ} = g l$
$T = m g + \frac{m v ^{2}}{l} = m g + \frac{m}{l} g l = 2 m g$
$∴ T = μ 4 m g$
$\Rightarrow μ = \frac{1}{2}$