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in Laws of motion by (15.2k points)
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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

2 Answers

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by (39.0k points)
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Best answer

(i) (D) -µv2/R

(ii) (C) \(\frac 1v = \frac 1{v_0} + \frac{\mu t}R\)

(iii) (D) v = v0

At any instant, say speed is v. Normal force against wall,

+1 vote
by (15.7k points)

(i) (D) -µv2/R

(ii) (C) \(\frac{1}{V} = \frac{1}{\text{v}_0} + \frac{\mu t}{R}\)

(iii) (D) v = v0

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