Question

Two blocks A and B of masses 10 kg and 15 kg are placed in contact with each other rest on a rough horizontal surface as shown in the figure. The coefficient of friction between the blocks and surface is 0.2. A horizontal force of 200 N is applied to block A. The acceleration of the system is: (Take $g=10m{s}^{-2}$)

• A. $4m{s}^{-2}$
• B. $6m{s}^{-2}$
• C. $8m{s}^{-2}$
• D. $10m{s}^{-2}$

Answer 1

The correct option is B $6m{s}^{-2}$

Here, Mass of block A, $m_A=10kg$
Mass of block B, $m_B=15kg$
Coefficient of friction between the blocks and the surface,
$\mu =0.2$
Applied force = 200 N
Force of friction on $A=\mu N_A=\mu m_{A}g=0.2\times 10\times 10=20N$
Force of friction on $B=\mu N_B=\mu m_{B}g=0.2\times 15\times 10=30N$
Taking two blocks forming one system, therefore net force acting on the blocks is
F = 200 - 20 - 30 = 150 N
Let a be common acceleration of the system.
$\therefore a=\frac{F}{m_A+m_B}=\frac{150N}{(10+15)}kg=6m{s}^{-2}$