A-stone-of-mass-100g-is-tied-to-the-end-of-a-string-of-50-cm-long-The-stone-is-whirled-as-a-conical-pendulum-so-that-it-rotates-in-horizontal-circle-radius-30-cm-Determine-the-angular-speed-and-the

Question Number 14677 by tawa tawa last updated on 03/Jun/17

A stone of mass 100 g is tied to the end of a string of 50 cm long . The stone is

whirled as a conical pendulum so that it rotates in horizontal circle radius

30 cm . Determine the angular speed and the tension in the string .

Answered by ajfour last updated on 03/Jun/17

h e i g h t o f c o n e g e n e r a t e d

i s h = \sqrt{l^{2} - r^{2}} = \sqrt{{(50)}^{2} - {(30)}^{2}} c m

= 40 c m

\tan θ = \frac{r}{h} = \frac{3}{4}; \sin θ = \frac{3}{5}

T \sin θ = m ω^{2} r

T \sin θ = m g

\Rightarrow \tan θ = \frac{ω^{2} r}{g}

o r ω = \sqrt{\frac{g \tan θ}{r}} = \sqrt{\frac{10 \times 3}{4 (0.30)}}

= 5 r a d / s

T = \frac{m g}{\sin θ} = \frac{0.1 \times 10}{(3 / 5)} = \frac{5}{3} N = 1.67 N .

Commented by ajfour last updated on 03/Jun/17

Commented by tawa tawa last updated on 03/Jun/17

I really appreciate your effort sir . God bless you sir .