An inclined plane makes an angle 30 horizontal . a solid sphere rolling down this.inclined.plane from rest without slipping has a linear acceleration equal to
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when a sphere rolls on an inclined plane then force of friction opposes its motion and acts in the direction opposite to the direction of motion. radius of sphere is R and mass of sphere is M. alpha is the angular acc. of the sphere
applying newtons second law of motion
Mgsintheta-f=Ma ................ 1
the net torque produced by the force of frction f*R=I*alpha ............2
I is the moment of inertia of sphere which is equal to 2MR^2/
a=alpha*R=>alpha=a/R .........3
putting value of alpha from eqn 3 in 2
f=Ia/R^2
putting this value of f in eqn 1
Mgsintheta-Ia/R^2=Ma
a=Mgsintheta/(M+I/R^2)
put the value of I=2MR^2/5
applying newtons second law of motion
Mgsintheta-f=Ma ................ 1
the net torque produced by the force of frction f*R=I*alpha ............2
I is the moment of inertia of sphere which is equal to 2MR^2/
a=alpha*R=>alpha=a/R .........3
putting value of alpha from eqn 3 in 2
f=Ia/R^2
putting this value of f in eqn 1
Mgsintheta-Ia/R^2=Ma
a=Mgsintheta/(M+I/R^2)
put the value of I=2MR^2/5
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