Question

Two trolleys of mass m and 3m are connected by a spring. They were compressed and released once, they move off in opposite direction and comes to rest after covering distances $S _ { 1 }$ and $S _ { 2 }$ respectively. Assuming the coefficient of friction to be uniform, the ratio of distances $S _ { 1 } : S _ { 2 }$ is

• A. 1 : 9
• B. 1 : 3
• C. 3 : 1
• D. 9 : 1

Answer 1

Answer: (D)

9 : 1

Answer 2

When trolley are released then they posses same linear momentum but in opposite direction. Kinetic energy acquired by any trolley will dissipate against friction.

$\therefore$ $\mu m g s = \frac { p ^ { 2 } } { 2 m }$ ⇒ $s \propto \frac { 1 } { m ^ { 2 } }$ [As P and u are constants]

⇒ $\frac { s _ { 1 } } { s _ { 2 } } = \left( \frac { m _ { 2 } } { m _ { 1 } } \right) ^ { 2 } = \left( \frac { 3 } { 1 } \right) ^ { 2 } = \frac { 9 } { 1 }$