Question

A thin rod of length $1m$ fixed in a vertical position inside a train, which is moving horizontally with constant acceleration $4m/s^2$. A bead can slide on the rod, and friction coefficient between them is $1/2$. If the bead is released from rest at the top of the rod, find the time when it will reach at the bottom. ($g=10m/s^2$)

• A. 1
• B. 0.5
• C. 2
• D. 3

Answer 1

The correct option is B 0.5

Consider, the mass of the bead is $m$

normal $nxm$ force between the rod and the bead is $4m$, where $m$ mass of the bead

So,

Friction force

$f=0.5\times 4m=2m$

Acceleration of the bead

$a=\frac{mg-2m}{m}=g-2=8m/s^2$

$u=0,a=8m/s^2,s=1m$

$\begin{array}{c}1=\frac{8\times t^2}{2}\\ t=0.5\sec \end{array}$

Hence, the time when it will reach at the bottom is $0.5sec$