A solid cylinder is rolling down on an inclined plane of angle θ , The coefficient of static friction between the plane and cylinder is μ s . Then condition for the cylinder not to slip is

Question

A solid cylinder is rolling down on an inclined plane of angle θ , The coefficient of static friction between the plane and cylinder is μ s . Then condition for the cylinder not to slip is (A)  tan θ ge 3μs (B)  tan θ >3μ s (C)  tan θ le 3μ s (D)  tan θ < 3μs

Tardigrade Admin · Accepted Answer

For the rolling of a solid cylinder acceleration

a = \frac{g}{3} sin θ

∴

The condition for the cylinder to remain in equilibrium

ma \leq μ_{s} R

\Rightarrow \frac{1}{3} M g sin θ \leq M g cos θ \cdot μ_{s}

or

μ_{s} \geq \frac{1}{3} tan θ

or

tan θ \leq 3 μ_{s}

Q. A solid cylinder is rolling down on an inclined plane of angle $θ,$ The coefficient of static friction between the plane and cylinder is $μ_{s}$ . Then condition for the cylinder not to slip is

$tan θ \geq 3 μ_{s}$

$tan θ > 3 μ_{s}$

$tan θ \leq 3 μ_{s}$

$tan θ < 3 μ_{s}$

For the rolling of a solid cylinder acceleration
$a = \frac{g}{3} sin θ$
$∴$ The condition for the cylinder to remain in equilibrium
$ma \leq μ_{s} R$
$\Rightarrow \frac{1}{3} M g sin θ \leq M g cos θ \cdot μ_{s}$
or $μ_{s} \geq \frac{1}{3} tan θ$
or $tan θ \leq 3 μ_{s}$

Q. A solid cylinder is rolling down on an inclined plane of angle θ, The coefficient of static friction between the plane and cylinder is μs​ . Then condition for the cylinder not to slip is

tanθ≥3μs​

tanθ>3μs​

tanθ≤3μs​

tanθ<3μs​