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In the given figure a ring of mass m is kept on a horizontal surface while a body of equal mass 'm' attached through a string, which is wounded on the ring. When the system is released the ring rolls without slipping. Consider the following statements and choose the correct option.

(i) acceleration of the centre of mass of ring is g/3
(ii) acceleration of the hanging particle is 2g/3
(iii) frictional force (on the ring) acts along forward direction
(iv) frictional force (on the ring) acts along backward direction
  • a)
    statement (i) and (ii) only
  • b)
    statement (ii) and (iii) only
  • c)
    statement (iii) and (iv) only
  • d)
    none of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In the given figure a ring of mass m is kept on a horizontal surface w...
Free body diagram of ring and mass is 

Since the ring is in pure rolling so its above point acceleration will be 2a and similarly acceleration of mass will be 2a.
The equation of motion of the system is
mg – T = m(2a)      ......(1)
T = ma        .......(2)
Substitute the value of T in equation (1)
mg - ma = 2ma
3ma = mg
a = g/3
So the acceleration of the center of the ring is, g/3
And acceleration of the hanging mass is 2a = 2g/3
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In the given figure a ring of mass m is kept on a horizontal surface while a body of equal mass m attached through a string, which is wounded on the ring. When the system is released the ring rolls without slipping. Consider the following statements and choose the correct option.(i) acceleration of the centre of mass of ring is g/3(ii) acceleration of the hanging particle is 2g/3(iii) frictional force (on the ring) acts along forward direction(iv) frictional force (on the ring) acts along backward directiona)statement (i) and (ii) onlyb)statement (ii) and (iii) onlyc)statement (iii) and (iv) onlyd)none of theseCorrect answer is option 'A'. Can you explain this answer?
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