Question

Two blocks $A$ and $B$ of mass $2\text{kg}$ and $4\text{kg}$ are placed one over the other. A horizontal force $F=2t$, which varies with time is applied on the upper block. If coefficient of friction between blocks $A$ and $B$ is 0.5 and horizontal surface is smooth. Then assuming $t$ is in seconds, the total time upto which both blocks will move together without slipping over each other is

• A. 5 sec
• B. 7.5 sec
• C. 10 sec
• D. 12.5 sec

Answer 1

The correct option is B 7.5 sec

If common maximum acceleration is ${}^{\prime }{a}^{\prime }$ then,
$(m_A+m_B)a=F$
$\Rightarrow (2+4)a=2t$
$\Rightarrow 3a=t\dots \dots \left(1\right)$
For block $B$, we have
$f_L=m_B\times a$
$\Rightarrow 0.5\times 2\times 10=4a$
$\Rightarrow a=2.5{\text{ms}}^{-2}$
From equation (1), we get
$t=7.5\text{sec}$
Hence, the correct answer is (b).