Question

A plank of mass $m_1=8kg$ with a bar of mass $m_2=2kg$ placed on its rough surface, lie on a smooth floor of elevator ascending g/4. The coefficient of friction is $\mu =1/5$ between, $m_{1}and{m}_2$ . A horizontal force F = 30 N is applied to the plank. Then the acceleration of bar and the plank in the reference frame of elevator are

• A. $3.5m/s^2,5m/s^2$
• B. $5m/s^2,\frac{50}{8}m/s^2$
• C. $2.5m/s^2,\frac{25}{8}m/s^2$
• D. $4.5m/s^2,4.5m/s^2$

Answer 1

The correct option is C $2.5m/s^2,\frac{25}{8}m/s^2$

let the frictional force between plank and bar is f

$f=\mu N$

N=pseudo force+weight of the bar

$N=20+\frac{2g}{4}=25N$

$f=25x1/5=5N$

acceleration of the bar = force on bar/mass of bar = frictional force/mass

$a=\frac{5}{2}$

$a=2.5m/s^2$

acceleration of the plank $a_1=30-\frac{5}{8}$

$a_1=\frac{25}{8}m/s^2$