Question

A particle slides along a track with elevated ends and a flat central part as shown in the figure. The flat part has a length $l=3m$. The curved portions of the track are frictionless. For the flat part the coefficient of kinetic friction is ${\mu }_k=0.2$. The particle is released at point $A$ which is at height $h=1.5m$ above the flat part of the track. Where does the particle finally come to rest?

• A. $1.5m$
• B. $2.0m$
• C. $2.5m$
• D. $3m$

Answer 1

The correct option is A $1.5m$

Here,

The body has initially total mechanical energy$=1.5mg$

After going through the frictional surface,

Loss in energy$=0.6mg$

Total energy when body goes left to right once$=0.9mg$

Total energy after body goes right to left again$=0.3mg$

Now the energy becomes zero midway in the frictional area,

Let us suppose the distance be $x$ from left,

$0.3mg-0.2mgx=0$

$x=1.5m$

Option $\text{A}$ is the correct answer.