Question

Three masses are connected as shown in figure on a horizontal frictionless surface and pulled by a force of $60\, N$. The tensions $T_{1}$ and $T_{2}$ are in the ratio

• A. $1:1$
• B. $1 : 5$
• C. $1 : 4 $
• D. $4 :5$

Answer 1

Answer: (B)

Horizontal component of force
$=60 \cos 30^{\circ}=30 \sqrt{3} N$

Acceleration of the system,
$a=\frac{\text { force }}{(3+12+15)}=\frac{30 \sqrt{3}}{30}=\sqrt{3} m / s ^{2}$
$\therefore T_{2}=$ mass pulled $\times$ acceleration
$=(3+12) \times \sqrt{3}=15 \sqrt{3} N$ and $T_{1}=3 \times \sqrt{3}=3 \sqrt{3} N$
$\therefore \frac{T_{1}}{T_{2}}=\frac{3 \sqrt{3}}{15 \sqrt{3}}=\frac{1}{5}$