Question

A cat of mass $m=1\text{kg}$ climbs on a rope hung over a light frictionless pulley as shown in the figure. A mass $M=2m$ lies on a smooth horizontal plane. What is the tension of the rope (in $\text{N}$) when the cat moves upwards with an acceleration $a=2{\text{m/s}}^2$ relative to the rope? (take $g=10m{s}^{-2}$)

Answer 1

${\overrightarrow{a}}_{cat/rope}={\overrightarrow{a}}_{cat}-{\overrightarrow{a}}_{Rope}=(2-a)$ upwards
Therefore, from FBD
$T-mg=m(2-a)......\left(1\right)$

Again,
$2T=2\times \frac{a}{2}.......\left(2\right)$
$\Rightarrow a=2T$
Put value of 'a' in eq....$\left(1\right)$, we get
$T-1\times 10=1(2-2T)$
$\Rightarrow T+2T=12$
$\Rightarrow 3T=12$
$\Rightarrow T=4\text{N}$