Question

A Smooth ring of Mass 'M' is threaded on a string as shown in the figure. Various portions of strings are vertical. What is the condition if the ring alone is to remain at rest –

• A. $\frac { 4 } { \mathrm { M } }$ = $\frac { 1 } { \mathrm {~m} }$ + $\frac { 1 } { \mathrm {~m} ^ { \prime } }$
• B. $\frac { 2 } { M }$ = $\frac { 1 } { \mathrm {~m} }$ + $\frac { 1 } { \mathrm {~m} ^ { \prime } }$
• C. $\frac { 1 } { \mathrm { M } }$ = $\frac { 1 } { \mathrm {~m} }$ + $\frac { 1 } { \mathrm {~m} ^ { \prime } }$
• D. $\frac { 3 } { M }$ = $\frac { 1 } { \mathrm {~m} }$ + $\frac { 1 } { \mathrm {~m} ^ { \prime } }$

Answer 1

Answer: (A)

$\frac { 4 } { \mathrm { M } }$ = $\frac { 1 } { \mathrm {~m} }$ + $\frac { 1 } { \mathrm {~m} ^ { \prime } }$

Answer 2

Since 'M' is at rest the tension in the string = $\frac { \mathrm { Mg } } { 2 }$ Let acceleration of m and m' is 'f' one will move downward and other will move upward

mg – $\frac { \mathrm { Mg } } { 2 }$ = mf ……..(i)

$\frac { \mathrm { Mg } } { 2 }$ – m'g = m'f …….(ii)

Solving equation (i) and (ii)

$\frac { 4 } { \mathrm { M } }$ = $\frac { 1 } { \mathrm {~m} }$ +