Question

In the figure shown, find the force exerted by the pulley at the support. Take $g=10{\text{m/s}}^2$ and assume that all surfaces are smooth.

• A. $21\text{N}$
• B. $42\text{N}$
• C. $21\sqrt{2}\text{N}$
• D. $\frac{21}{\sqrt{2}}\text{N}$

Answer 1

The correct option is C $21\sqrt{2}\text{N}$

$a=\frac{\text{Supporting Force}}{\text{Total mass}}=\frac{3g}{10}=3{\text{m/s}}^2$

$T=7a=7\times 3=21\text{N}$
Since the tensions act tangentially at the pulley while force at the support makes equal angle with both the tensions i.e. ${45}^{\circ }$
Therefore, force exerted by the pulley at the support,
$F\cos {45}^{\circ }=T$
$\Rightarrow F=21\sqrt{2}\text{N}$