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 0.12g? (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 0.12g?

Explanation:

required acceleration = .12 g

acceleration of a rolling body on an inclined surface is given by the expression

= gsinθ / 1 + k² / R²

θ is the slope, k is radius of gyration of rolling body , R is radius of the rolling body .

Here rolling body is sphere

k² = 2/5 R²

k² / R² = 2/5

acceleration = g sinθ / 1 + k² / R²

.12 g = g sinθ / 1 + k² / R²

.12 g =g sinθ / 1 + 2/5

.12 = sinθ / 1.4

sinθ = .168

θ = 9.6 degree .

b ) If a frictional block falls down the incline , its acceleration will be

g sinθ = g sin 9.6

= 0.167 g . which is more than 0.12 g .

.) the observation by semmelweis that more mothers died of childbed fever when their doctors also worked in the morgue

the displacement produced by the body.  

the amount of force subjected to the body.  

the angle between the direction of force and displacement