Question

A small particle slides along a track with elevated ends and a flat central part as shown in figure. The flat part has a length of 3m and the curved portions of the track are frictionless. For the flat part, coefficient of kinetic friction is $\mu$ = 0.2. The particle is released at a point A, which is at a height 0.3 m above the flat part of track. The position where the particle finally come to rest is :

• A. left to mid point of the flat part
• B. right to the mid point of the flat part
• C. mid point of the flat part
• D. none of these

Answer 1

The correct option is C mid point of the flat part

Velocity of block when it enters into the flat surface -

$\frac{1}{2}m{u}^2=mgh=m\left(10\right)\left(0.3\right)$ $⟹u^2=6$

Now from flat part, its deacceleration due to friction is $a=-\mu g=-0.2\left(10\right)=-2m/s^2$

Using the equation - $v^2=u^2+2as$

$0=6-2\left(2\right)s$ $⟹s=1.5m$