Question

Consider the shown arrangement. The coefficient of friction between the two blocks is 0.5. There is no friction between the 4 kg block and the horizontal surface. If a horizontal force of 12 N is applied on the 2 kg block as shown in the figure, the acceleration of the 4 kg block would be

• A. $2.5m/s^2$
• B. $2m/s^2$
• C. $5m/s^2$
• D. $10m/s^2$

Answer 1

The correct option is A $2.5m/s^2$

Refer image 1.

$N=2g$

$N=20Newtons$

$f_s=N\times l$

$=\left(20\right)\left(0.5\right)$

$=10Newtons$

$f-f_s=2a$

$12-10=2a$

$\Rightarrow a=1m/s^2$

Refer image 2.

$f_s=4a$

$10=4a$

$\Rightarrow a=\frac{10}{4}=2.5m/s^2$