Question

A $5\text{kg}$ block has a rope of mass $2\text{kg}$ attached to its underside and a $3\text{kg}$ block is suspended from the other end of the rope. The whole system is accelerated upward at $2{\text{ms}}^{-2}$ by an external force $F_0$.

What is the tension at middle point of the rope and $F_0$? $(g=10{\text{ms}}^{-2})$

• A. $48\text{N},100\text{N}$
• B. $48\text{N},120\text{N}$
• C. $100\text{N},120\text{N}$
• D. $20\text{N},100\text{N}$

Answer 1

The correct option is B $48\text{N},120\text{N}$

For calculating the value of $F_0$, consider two blocks with the rope as a single system.
F.B.D. of whole system

$F_0-100=10\times 2$
$\Rightarrow F_0=120\text{N}$
For calculating tension at the midlle point we draw F.B.D. of $3\text{kg}$ block with half of the rope (mass $1\text{kg})$ as shown. So, total mass becomes $4\text{kg}$.

$T-4g=4\left(2\right)$
$\Rightarrow T=48\text{N}$