Answer:
Explanation:
Let the frictional force required be f .
frictional force is responsible in creating rotational motion in the cylinder.
torque created by frictional force = f R
if angular acceleration be α
α = f R / I , I is moment of inertia of cylinder .
α = a / R , a is linear acceleration.
f R / I = a / R
a = f R² / I
linear acceleration a of cylinder down the slope
ma = mgsinθ - f , ( f force is acting upwards and mgsinθ is acting downwards )
mf R² / I = mgsinθ -f
f ( m R² / I + 1) = mgsinθ
f = mgsinθ / ( m R² / I + 1)
= mgsinθ / ( m R² / mk² + 1) , k is radius of gyration of cylinder.
= mgsinθ / ( R² / k² + 1)
Putting the given values
f = Mgsinβ /( R² / k² + 1)
for cylinder , R² / k² = 2
f = Mgsinβ /3
