Question

A body of 10 kg is suspended by a rope and is pulled to a side by means of a horizontal force 10√3 kg wt. Then find the angle made by the rope to the vertical. ​

Answer 1

First, draw the figure as per the question requirement.

Concept

• mention all the forces which are being applied on the mass.
• the angle made by the resultant of forces will be the angle made by the rope from vertical.

Solution

Given:

• $\rm F_1 = 10\sqrt{3} \: kgwt = 10\sqrt{3}\: g \: Newtons$
• $\rm F_2 = mg = 10 \: g \: Newtons$

As we see in the triangle in attached image:

$\to\rm tan\theta = \dfrac{perpendicular}{base}$

$\to\rm tan\theta = \dfrac{10\sqrt{3}\: g}{10\: g}$

$\to\rm tan \theta = \sqrt{3}$

$\implies \bf \theta = 60\degree$

★ so angle made by the rope from vertical is 60°