Question

In the figure shown, all surfaces are smooth. Find force acting between $4kg$ and $10kg$ blocks:

• A. $70N$
• B. $10N$
• C. $60N$
• D. $100N$

Answer 1

The correct option is A $70N$

By applying force balance equation on all the three free masses

The acceleration of all the three masses $=a$

Let all the three masses are a system of $20kg$ moving in one direction

So, the acceleration of all the masses is same is same as combined mass

$a=\frac{netforce}{totalmass}a=\frac{100-40}{6+4+10}=\frac{60}{20}=3$

Apply force balance equation for mass $6kg$,

$100-N_1=6\times 3100-N_1=18N_1=82Nformass4kg{N}_1-N_2=4\times 3N_1-N_2=12here{N}_1=82Nthen,N_2=82-12=70N$

The force acting between $4kg$ and $10kg$ =$N_2$=$70N$