Question

A mass$Mkg$ is suspended by a weightless string. The horizontal force required to hold the mass at$60°$ with the vertical is

• A. $Mg$
• B. $Mg\sqrt{3}$
• C. $Mg\left(\sqrt{3}+1\right)$
• D. $\frac{Mg}{\sqrt{3}}$

Answer 1

The correct option is B

$Mg\sqrt{3}$

Step 1. Given data

A mass$Mkg$ is suspended by a weightless string

Angle with the vertical, $=60°$

Step 2. Finding the force, $F$

The tension acting on the string at equilibrium is$T$ and the applied force is $F$

Balancing the forces

In the horizontal direction: $F=T\sin 60°$ ____$\left(1\right)$

In the vertical direction: $Mg=T\cos 60°$ ____$\left(2\right)$

Dividing equation $\left(1\right)by\left(2\right)$, we get: $\frac{F}{Mg}=\tan 60°$

Therefore, $F=Mg\surd 3$

Hence, option ($B$) is correct.