Question

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 $\frac { 2 \mathrm {~g} } { 3 }$

(ii) Acceleration of the hanging particle is $\frac { 4 \mathrm {~g} } { 3 }$

(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 (i) and (iii)only
• C. Statement (ii) and (iv) only
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

.(4)

Sol.

T × 2R = 2mR²a

T = mRa ....(1)

mg – T = m × 2a ....(2)

a = R a ....(3)

mg = 3 ma $\mathrm { a } = \frac { \mathrm { g } } { 3 }$ =

Acceleration of ring .

Acceleration of block = $\frac { 2 \mathrm {~g} } { 3 }$

T – f_r = ma

m Ra – f_r = ma

$\mathrm { f } _ { \mathrm { r } } = 0$