Question

A bead of mass $m$ is fitted on to a rod and can move on it without friction. Initially the bead is at the middle of the rod and the rod moves translationally in a horizontal plane with an acceleration $a_o$ in a direction forming an angle $\alpha$ with the rod. The downward acceleration of bead with respect to rod is

• A. $gsin\alpha$
• B. $(g+a_0)\sin \alpha$
• C. $g\sin \alpha +a_0\cos \alpha$
• D. $g\sin \alpha -a_0\cos \alpha$

Answer 1

The correct option is D $g\sin \alpha -a_0\cos \alpha$

Let the mass of bed $=m$

Let the acceleration of bead $=a_b$

Observing from the observer moving with rod

Then a pseudo force $F=ma$ is applied on the bead in opposite direction of acceleration of rod

Now making FBD,

bead is not moving perpendicular to rod

$N=mg\cos \alpha -ma\sin \alpha$

Along the length of rod

Let the acceleration of rod along rod $=a_b$

$\Rightarrow mg\sin \alpha -mg\cos \alpha =m{a}_r$

$\Rightarrow a_r=g\sin \alpha -a\cos \alpha$