Question

In the figure shown, find the tension $T_1$, if all surfaces are smooth. Take $g=10{\text{m/s}}^2$.

• A. $20\text{N}$
• B. $30\text{N}$
• C. $50\text{N}$
• D. $60\text{N}$

Answer 1

The correct option is D $60\text{N}$

Downward force on $10\text{kg}=10g$
Downward force on $4\text{kg}=4g\sin {30}^{\circ }=2g$
(down the incline)

Hence, acceleration of the system is given by $a=\frac{\text{Supporting Force}-\text{Opposing Force}}{\text{Total mass}}$
$\frac{10g-2g}{20}=4{\text{m/s}}^2$

We have, from equation of equilibrium of $10\text{kg}$ block,
$10g-T_1=10a$
$\Rightarrow T_1=10(g-a)=60\text{N}$