Question

Two blocks one of mass $A=1kg$ and $B=2kg$. A force of $5N$ is applied on $A$ (see figure). Coefficient of friction between $A$ and $B$ is $0.2$ and that of between $B$ and horizontal surface is zero. Find acceleration of $A$ and $B$

• A. $5m/s^2$ and $3m/s^2$
• B. $6m/s^2$ and $2m/s^2$
  
• C. $3m/s^2$ and $1m/s^2$
  
• D. $2m/s^2$ and $2m/s^2$
  

Answer 1

The correct option is C $3m/s^2$ and $1m/s^2$

There can be two cases

Case:1 if friction is sufficient then both the blocks will move together with same acceleration.

Case:2 frction reaches its maximum value and blocks will move with differemt acceleration.

Maximum friction between block A and B is $=\mu .N$

$N=m_a.g$

So maximum friction is 2N.

Acceleration if both blocks move togther $5=3.a$

Force reqired to produce acceleration of $1.66m/s^2$for block B is $m.a$ $=3.33N$

But maximum frictional force available is 2N.

So both blocks will move with different acceleration.

Now $F_f=2$ and acc. of block B is

$2=2.a_B$

$a_B=1m/s^2$

And acc. of block A is

$a_A.1=F-F_f$

$a_A=3m/s^2$.