Question

A thin rod of length $1m$ is fixed in a vertical position inside a train which is moving horizontally with a constant acceleration of $4m/s^2$. A bead can slide on the rod and the friction co-efficient 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.

• A. $3/2sec$
• B. $1sec$
• C. $2sec$
• D. $1/2sec$

Answer 1

The correct option is D $1/2sec$

From FBD of bead, $N=m{a}_0=4m$
and $ma=mg-\mu N$ or $ma=10m-\left(1/2\right)4m=8m$ or $a=8m/s^2$
using $S=ut+\frac{1}{2}a{t}^2$, we get $1=0t+\frac{1}{2}8t^2$
or $t^2=1/4\Rightarrow t=\frac{1}{2}sec$