Question

A uniform solid sphere rolls down an incline. (a) What must be the incline angle (deg) if the linear acceleration of the center of the sphere is to have a magnitude of 0.14g? (b) If a frictionless block were to slide down the incline at that angle, would its acceleration magnitude be more than, less than, or equal to 0.14g?

Answer 1

here,

(a)

let the mass of the sphere be m

the accelration , a = net force /( effective mass)

a = m *g* sin(theta)/( m + I/r^2)

a = m *g* sin(theta)/( m + ( (2/5 * m * r^2)/r^2)

0.14 g = g* sin(theta)/( 1 + 0.4)

theta = 11.3 degree

the angle of incline is 11.3 degree

b)

if the incline is friction less

the effective mass is less ,

so the accelration is more