Question

Two ring of mass m and 2 m are connected with a mass less spring and can slips over two frictionless parallel horizontal rails as shown in figure. Ring of mass m is given velocity 'v₀' in the direction shown. Maximum stretch in spring will be –

• A. $\sqrt { \frac { \mathrm { m } } { \mathrm { k } } } \mathrm { v } _ { 0 }$
• B. $\sqrt { \frac { 3 \mathrm {~m} } { \mathrm { k } } } \mathrm { v } _ { 0 }$
• C. $\sqrt { \frac { 2 \mathrm {~m} } { 3 \mathrm { k } } } \mathrm { v } _ { 0 }$
• D. $\sqrt { \frac { 2 \mathrm {~m} } { \mathrm { k } } } \mathrm { v } _ { 0 }$

Answer 1

Answer: (C)

$\sqrt { \frac { 2 \mathrm {~m} } { 3 \mathrm { k } } } \mathrm { v } _ { 0 }$

Answer 2

Maximum expansion in spring is given by

$\frac { 1 } { 2 } \mathrm { kx } _ { \max } ^ { 2 }$ = $\frac { 1 } { 2 } \mu v _ { 0 } ^ { 2 }$

[m = Reduced mass]

̃ x_max = $\sqrt { \frac { \mu } { \mathrm { k } } }$ . v₀

= $\sqrt { \frac { 2 \mathrm {~m} } { 3 \mathrm { k } } }$ v