A solid cylinder of mass M and radius R rolls down an inclined plane which has an angle of inclination θ . Find the acceleration of this rolling cylinder if it rolls without slipping.

Question

A solid cylinder of mass M and radius R rolls down an inclined plane which has an angle of inclination θ . Find the acceleration of this rolling cylinder if it rolls without slipping. (A) (1/23)gsin θ  (B) (2/3)gsin θ  (C) (2/5)gsin θ  (D) (2/7)gsin θ

Tardigrade Admin · Accepted Answer

Acceleration of a rolling body down an inclined plane is a=(g sin θ /1 + (K2)R2) For solid cylinder, K2=(R2/2) ∴ a=(g sin θ /1 + (1)2)=(2/3)gsin â¡ θ

Q. A solid cylinder of mass $M$ and radius $R$ rolls down an inclined plane which has an angle of inclination $θ$ . Find the acceleration of this rolling cylinder if it rolls without slipping.

$\frac{1}{23} g s in θ$

$\frac{2}{3} g s in θ$

$\frac{2}{5} g s in θ$

$\frac{2}{7} g s in θ$

Acceleration of a rolling body down an inclined plane is $a = \frac{g s in θ}{1 + \frac{K ^{2}}{R ^{2}}}$
For solid cylinder, $K^{2} = \frac{R ^{2}}{2}$
$∴ a = \frac{g s in θ}{1 + \frac{1}{2}} = \frac{2}{3} g s in θ$

Q. A solid cylinder of mass M and radius R rolls down an inclined plane which has an angle of inclination θ . Find the acceleration of this rolling cylinder if it rolls without slipping.

231​gsinθ

32​gsinθ

52​gsinθ

72​gsinθ