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A solid sphere of mass 0.5 kg is kept on a horizontal surface. The coefficient of static friction ( ) between surfaces in contact is . What maximum force can be applied at the highest point in the horizontal direction so that the sphere doesn't slip on the surface? Round the answer to the nearest integer.
The answer is 3.
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1 solution
I don't know how to upload a picture so here is my solution without diagram. Let 'F' force act on the top of sphere towards right and 'f' (frictional force) act on it towards left and mg vertically downwards and N vertically upwards.
Equation in vertical direction m g = N
Equation in horizontal direction F − μ m g = m a
Rotational equation F R + μ m g R = I α
As the motion of the ball is pure rolling
so a = r α
Here I = 5 2 m R 2
On solving we get * F ≈ − 3 N
negative sign shows that the direction of 'F' should have been towards left.