Question

A $4kg$ block is attached to a vertical rod by means of two strings of equal length. When the system rotates about the axis of the rod, the strings are extended as shown in figure.
a) How many revolutions per minute must the system make in order for the tension in the upper cord to be $20kg?$
b) What is the tension in the lower cord then?

• A. $39.6rpm$
• B. $49.6rpm$
• C. $396rpm$
• D. $3960rpm$

Answer 1

The correct option is A $39.6rpm$

The tension in the lower wire $T_2=150N$ (solved earlier)

Also $sin\theta =\frac{4}{5}$ and $cos\theta =\frac{3}{5}$ (solved earlier)

Given : $m=4$ kg, $T_1=200$ N

Horizontal direction : $m{a}_r=T_{1}cos\theta +T_{2}cos\theta$

$\therefore$ $mr{w}^2=(T_1+T_2)cos\theta$ where $r=OA=3$ m

$\therefore 4\times 3w^2=(200+150)\times \frac{3}{5}$

$⟹w=4.18$ N

Using $2\pi f=w$

$\therefore 2\pi f=4.18$

$⟹f=0.67$ rps

$⟹f=0.67\times 60=39.6$ $rpm$