Question

Find the ratio of tension $T_1$ and $T_2$ in the string as shown in figure if the whole system is moving with constant acceleration of $4m/s^2$ under the influence of force of magnitude $220N$ acting on block of mass $15kg$ . Assume the coefficient of friction to be $\mu =1/3$ and $g=10m/s^2$.

• A. $0.35$
• B. $0.45$
• C. $0.2$
• D. $5$

Answer 1

The correct option is C $0.2$


Since the whole system is having acceleration $4m/s^2$, individual body will also have an acceleration $4m/s^2$.
FBD of block of mass $3kg$,


$T_1-f_1=ma$
$T_1-\mu mg=ma\Rightarrow T_1=(3\times 4)+(\frac{1}{3}\times 3\times 10)$
$\begin{array}{}\Rightarrow T_1=22N& \text{(1)}\end{array}$
FBD of block of mass $15kg$,


$220-T_2-f_2=ma$
$T_2=220-\mu mg-ma\Rightarrow T_2=220-(\frac{1}{3}\times 15\times 10)-(15\times 4)$
$\begin{array}{}\Rightarrow T_2=110N& \text{(2)}\end{array}$
From $\left(1\right)$ and $\left(2\right)$,
$\frac{T_1}{T_2}=\frac{22}{110}=0.2$