Rolling Down An Incline (numerical)

Question

A solid cylinder is released from rest and rolls without slipping down an incline making an angle whose sine equals 0.30, with gravitational acceleration taken as 10 m/s². What is its linear acceleration?

RankGuru · Accepted Answer

Building on NCERT Class 11, Chapter 7 (System of Particles and Rotational Motion), a body rolling without slipping down an incline has linear acceleration a = g sinθ / (1 + k²/R²), where the denominator accounts for the share of gravitational energy that must be diverted into rotational motion rather than pure translation. The term k²/R² is the dimensionless shape factor, equal to the square of the radius of gyration divided by the square of the radius. For a uniform solid cylinder this factor is k²/R² = ½, so the denominator becomes 1 + ½ = 3/2. Substituting the given quantities yields a = (10 × 0.30) / (3/2) = 3 / 1.5 = 2 m/s². The option 3 m/s² is the value g sinθ alone would give if the cylinder slid frictionlessly without rotating, which ignores rotational inertia entirely. The option 1 m/s² over-divides the result and assumes an incorrect shape factor. The option 5 m/s² has no valid derivation from the given data. A plausibility check confirms that the rolling acceleration of 2 m/s² is correctly smaller than the frictionless sliding value of 3 m/s², which is exactly what we expect because some of the available energy must go into spinning the cylinder up rather than translating it.

Rolling Down An Incline (numerical)

Select the correct option:

🔒 Solution Hidden from View

More rotational motion Practice Questions

A thin circular ring of mass M and radius R has a moment of inertia MR² about its central axis perpe...

A uniform beam of weight 200 N and length 4 m rests horizontally on two supports placed at its two e...

A point on the rim of a wheel of radius 0.50 m moves while the wheel rotates at a constant angular v...

A bomb at rest in deep space suddenly explodes into several fragments that fly off in different dire...

A constant torque of 5 N·m acts on a wheel and turns it through an angular displacement of 8 radians...

A solid sphere and a thin spherical shell have the same mass and the same radius and rotate about th...

A child of negligible spin sits on a rotating stool that turns at 2 rad/s with moment of inertia 4 k...

A force is applied to a particle whose position vector relative to the origin is given, and the forc...

A flywheel starts from rest and attains an angular velocity of 60 rad/s in 12 seconds under a consta...

A disc with moment of inertia 0.5 kg·m² rotates about its central axis at an angular velocity of 4 r...

A grinding wheel with moment of inertia 2 kg·m² experiences a constant net torque of 10 N·m about it...

A rigid body of mass 8 kg has a moment of inertia of 32 kg·m² about a particular axis of rotation. W...

About This Question

Solution