In a rotor, a hollow vertical cylindrical structure rotates about its axis and a person rests against the inner wall.

Question

Comprehension Type Questions

Passage In a rotor, a hollow vertical cylindrical structure rotates about its axis and a person rests against the inner wall. At a particular speed of the rotor, the floor below the person is removed and the person hangs resting against the wall without any floor. If the radius of the rotor is 2m and the coefficient of static friction between the wall and the person is 0.2. Find the following parameters and relations.

(i) If v is the velocity of rotation of rotor and N be the reaction of wall, then-

(A) N = mg

(B) \(\vec F = \vec F_1 + \vec F_2\) \(\Rightarrow\) |\(\vec F\)| = \(\sqrt{10^2 + 5^2 + 2.10.5 cos 120^\circ} = 5\sqrt{3} N\)

(C) N = \(\sqrt{(mg)^2 + \left(\frac{mv^2}{r}\right)^2}\)

(D) None of these

(ii) In order to man remain in equilibrium we must have

(A) µ = mg N 

(B) 2 f mg = µ 

(C) µ = N mg 

(D) None of these

(iii) The value of velocity will be given by –

(A) v = \(\sqrt{\mu rg}\)

(B) v = \(\sqrt{\frac{rg}{\mu}}\)

(C) v = \(\sqrt{\frac{g}{\mu r}}\)

(D) v = \(\sqrt{\frac{\mu g}{r}}\)

Answer 1

(i) (B) \(\vec F = \vec F_1 + \vec F_2 ⇒ |\vec F| = \sqrt{10^2 + 5^2 + 2.10.5 \cos120°} = 5\sqrt 3N\) 

(ii) (C) µ = N mg

(iii) (B) v = \(\sqrt{\frac {rg}{\mu}}\)

Answer 2

(i) (B)   \(\vec F = \vec F_1 + \vec F_2\) \(\Rightarrow\) |\(\vec F\)| = \(\sqrt{10^2 + 5^2 + 2.10.5 cos 120^\circ} = 5\sqrt{3} N\)

(ii) (C) µ = N mg 

(iii) (B) v = \(\sqrt{\frac{rg}{\mu}}\)