Comprehension Type Questions
Passage : A block of mass m moves on a horizontal circle against the wall of a cylindrical room of radius R. The floor of the room on which the block moves is smooth but the friction coefficient between the block and the side wall is µ . The block is given initial velocity v0 . Then answer the following questions.
(i) What is the tangential acceleration of the block?
(A) µg
(B) -µg
(C) µv2/R
(D) -µv2/R
(ii) What is the value of velocity v as the function of time t?
(A) \(\frac{1}{V} = \frac{1}{\text{v}_0} + \frac{\mu t}{2R}\)
(B) \(\frac{1}{V} = \frac{1}{\text{v}_0} - \frac{\mu t}{2R}\)
(C) \(\frac{1}{V} = \frac{1}{\text{v}_0} + \frac{\mu t}{R}\)
(D) \(\frac{1}{V} = \frac{1}{\text{v}_0} - \frac{\mu t}{R}\)
(iii) What is the value of velocity v as the function of distance x travelled on the circumference?
(A) v = v0 e\(\frac{2 \mu}{R}\)
(B) v = v0 e\(\frac{\mu}{R}{\text{x}}\)
(C) v = v0\(\left( 1 - e^{\frac{2\mu}{R}{\text x}}\right)\)
(D) v = v0