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
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
$1:9$
$1:3$
$3:1$
$9:1$
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
When trolley are released then they posses same linear momentum but in opposite direction. Kinetic energy acquired by any trolley will dissipate against friction.
$\therefore \mu \,mg\,s = \frac{{{p^2}}}{{2m}}$ $⇒$ $s \propto \frac{1}{{{m^2}}}$ [As $P$ and $u$ are constants]
$⇒$ $\frac{{{s_1}}}{{{s_2}}} = {\left( {\frac{{{m_2}}}{{{m_1}}}} \right)^2} = {\left( {\frac{3}{1}} \right)^2} = \frac{9}{1}$