Question

Block A of mass $35\text{kg}$ is resting on a frictionless floor. Another block B of mass $7\text{kg}$ is resting on it as shown in the figure. The coefficient of static friction between the blocks is $0.5$ while kinetic friction is $0.4$. If a force of $100\text{N}$ is applied to block B, the acceleration of the block A will be $(g=10{\text{ms}}^{-2}):$

• A. $0.8{\text{ms}}^{-2}$
• B. $2.4{\text{ms}}^{-2}$
• C. $0.4{\text{ms}}^{-2}$
• D. $4.4{\text{ms}}^{-2}$

Answer 1

The correct option is A $0.8{\text{ms}}^{-2}$

Maximum force for which both blocks move together is
$F_{max}=\frac{m_1}{m_2}{\mu }_s(m_1+m_2)g$
$F_{max}=\frac{7}{35}0.5\left(42\right)10=42\text{N}$
Given $F=100\text{N}$
Hence relative-slipping occurs between A and B
Only force acting on block B is kinetic friction
$f_k={\mu }_{k}N=0.4\left[70\right]=28\text{N}$
Hence acceleration of the $35\text{kg}$ block
$a=\frac{28}{35}=\frac{4}{5}=0.8{\text{ms}}^{-2}$