Question

EE(Main)-Physics
9. A string of length 0.1 m cannot bear a tension
more than 100N. It is tied to a body of mass 100g
and rotated in a horizontal circle. The maximum
angular velocity is ........
(1) 100 rad/s
(2) 1000 rad/s
(3) 10000/s
(4)0.1 rad/s
​

Answer 1

Answer:

At critical condition

Tension in string =100N

or,mw^2r=100

or,0.1*w^2*0.1=100

or,w=100 rad/s

Answer 2

Answer:

Angular velocity $\varpi = 100\ rad/sec$

Explanation:

Since when a string of length 0.1 m is rotated in a horizontal circle its length become a radius of circle, and it also experience a centripetal force which is required condition for performing a uniform circular motion.

So,$F_{c} = m\frac{v^{2} }{r}$...........................(1)

since we know that $v = r \varpi$.....................(2)

from (1) and (2) we get

$F_{c} = mr{\varpi{2} }$

Here tension is equals to the centripetal force

so, angulr velocity is

$100 = 0.1\times 0.1\times \varpi^{2}$

$\varpi = 100\ rad/sec$