Question

Two blocks of masses $6kg$ and $4kg$ connected by a rope of mass $2kg$ are resting on a frictionless floor as shown in the figure. If a constant force $60N$ is applied to the $6kg$ block, find the tension in the rope at points $A,B$ and $C$. $B$ is at the mid-point and points $A$ and $C$ are at the ends. Assume that the mass of the rope is uniformly distributed along its length.

• A. $30N,25N,20N$ respectively
• B. $20N,20N,30N$ respectively
• C. $30N,20N,25N$ respectively
• D. None of the above

Answer 1

The correct option is A $30N,25N,20N$ respectively

$F_{net}=60N$

Total mass of the system
$M_s=12kg$

Acceleration of the system
$a_s=\frac{60}{12}=5m/s^2$


$a=\frac{F_{net}}{m}$

$\Rightarrow 5=\frac{60-T_A}{6}$

$\Rightarrow 30=60-T_A$

$\Rightarrow T_A=30N$


$a=\frac{F_{net}}{m}$

$\Rightarrow 5=\frac{T_C}{4}$

$\Rightarrow T_C=20N$

For the midpoint B, block of mass $4kg$ and half of the rope (mass $1kg$) can be treated as one system of mass $5kg$


$a=\frac{T_B}{5}$
$\Rightarrow T_B=25N$