A sphere is rotating between two rough inclined walls as shown in figure. Coefficient of friction between each wall and the sphere is 1 3 . If f 1 and f 2 be the frictional forces at P and Q . Then f 1 f 2 is

Step-by-step solution

Let μ be the friction coefficient between sphere and each wall. Free body diagram of sphere is Net force on the sphere in horizontal diarection is zero. ∴ N 1 cos 60 ο + μ N 2 cos 60 ο = N 2 cos 30 ο + μ N 1 cos 30 ο ⇒ N 1 + μ N 2 = 3 N 2 + μ N 1 ⇒ N 1 1 - 3 μ = N 2 3 - μ ⇒ N 1 N 2 = 3 - μ 1 - 3 μ Substituting μ = 1 3 we get, ⇒ N 1 N 2 = 3 - 1 3 1 - 3 3 = 3 3 - 1 3 - 3 = 1 + 4 3 ⇒ f 1 f 2 = μ N 1 μ N 2 = 1 + 4 3