Question

A body of mass `200g` tied to one end of string is revolved in a horizontal circle of radius `50cm` with angular speed `60` revolution per minute `("rpm")` on a smooth horizontal surface. Find (a) linear speed, (b) the acceleration and ( c) tension in the sting. what will happen if string is broken? (Take `pi^(2)=10)`

Answer 1

Angular speed, `omega=(2pin)/(60)=(2pixx60)/(60)`
`=2pi"rad s"^(-1)=6.28"rad s"^(-1)`
Horizontal component of the tension, `T_(H)=T sintheta`,
vertical component of tension, `T_(V)=Tcostheta=mg`

(a) Linear speed `v=romega=0.5xx2pi=pims^(-1)=3.14ms^(-1)`
(b) Asseleration `a_(c)=(v^(2))/(r)=((pi)^(2))/(0.5)~~(10)/(0.5)=20ms^(2)`
(c) Horizontal component of tension `T_(H)=(mv^(2))/(r)=0.2xx20=2N`
When the string is broken, tension `T_(H)` (i.e., centripetal force vanishes and body moves along the tangent in a staight line with wpeed `3.14ms^(-1)`.