Question

Three masses are connected as shown in figure on a horizontal frictionless surface and pulled by a force of $60N$. 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 $T_1=3\times \sqrt{3}=3\sqrt{3}N$
$\therefore \frac{T_1}{T_2}=\frac{3\sqrt{3}}{15\sqrt{3}}=\frac{1}{5}$