Question

Two blocks of masses $4\text{kg}$ and $2\text{kg}$ are connected by a light string and placed on rough horizontal plane. The $2\text{kg}$ block is pulled with a constant force $F$ as shown in the figure. The coefficient of friction between the blocks and the ground is $0.5$. What is the value of $F$ so that tension in the string is constant throughtout the motion of the blocks?

• A. $40\text{N}$
• B. $30\text{N}$
• C. $45\text{N}$
• D. $60\text{N}$

Answer 1

The correct option is B $30\text{N}$

For the tension in the string to be constant, net force should be zero and so does the acceleration.

For $a=0$, tension is constant throughout.
Net force $=F-f=0$, $F=f=f_1+f_2$ where $(f_1,f_2)$ are the frictional force on the block $4\text{kg}$ and $2\text{kg}$

$F_{net}=\mu \times (4+2)\times g=0.5\times 6\times 10=30\text{N}$

The correct option is (b)