Question

A mass of M kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of ${45}^o$ with the initial vertical direction:

• A. $Mg(\sqrt{2}-1)$
• B. $Mg\sqrt{2}$
• C. $\frac{Mg}{\sqrt{2}}$
• D. None of these

Answer 1

The correct option is C $\frac{Mg}{\sqrt{2}}$

tan⁡45∘ =fmg ⇒f=mg2 $$\begin{array}{c}\tan {45}^{\circ }=\frac{f}{mg}\\ \Rightarrow f=\frac{mg}{\sqrt{2}}\end{array}$$tan45∘ =mgf​ ⇒f=2​ mg​ ​

Hence, the options $C$ is the correct answer.