Question

A block of mass $1\text{k}g$ rests on a plank of mass $2\text{k}g$ as shown in the figure. The coefficients of friction between block and plank are ${\mu }_s=0.75$ and ${\mu }_k=0.60$. The plank rests on a frictionless surface. The maximum force $F$ that can be applied , if the block is not to slide on the plank is

• A. $5.5\text{N}$
• B. $6.5\text{N}$
• C. $7.5\text{N}$
• D. $8.5\text{N}$

Answer 1

The correct option is A $5.5\text{N}$

Block and plank must have common acceleration in order to move together and the block to not to slide on the surface of plank.

FBD of block as shown,


Using Newton's second law of motion we can write,

$f-F=ma$

$f-F=a$

${\mu }_{s}mg-F=a$

$0.75\times 1\times 10-F=a$

$7.5-F=a$.......(i)

FBD of plank as shown,

$2F-f=ma$

$2F-f=2a$

$2F-{\mu }_{s}mg=2a$

$2F-0.75\times 1\times 10=2a$

$2F-7.5=2a$.......(ii)

From (i) and (ii),

$15-7.5=4a$

$\therefore a\approx 2\text{m}/{\text{s}}^2$

Substituting the value of $a$ in eq(i) we get,

$7.5-F=2$

$\therefore F=5.5\text{N}$