Question

A particle of mass $m$ slides along a curved-flat-curved track. The curved portions of the track are smooth. If the particle is released at the top of one of the curved portions, the particle comes to rest at the flat portion of length $l$ and of $\mu ={\mu }_{kinetic}$ after covering a distance of:

• A. $\frac{l}{3\mu }$
• B. $\frac{H}{2{\mu }_{kinetic}}$
• C. $\frac{l}{6}$
• D. $\frac{H}{{\mu }_{kinetic}}$

Answer 1

The correct option is D $\frac{H}{{\mu }_{kinetic}}$

Here $PE=$ Work done friction force
$mgH={\mu }_{kinetic}mgS$

or $S=\frac{H}{{\mu }_{kinetic}}$
The particle cover the length $l$ or not or covers it repeatedly is determined by the above relation.