Question

an object of mass 0.5kg attach to a string of length 0.5m is whirled in vertical circle at constant angular speed if the maximum tension in the string is 5kgwt calculate speed of object

Answer 1

Given: Mass of object = m = 0.5 kg, Radius of circle = r = 0.5 m, Tension in the string = T = 5 kg wt = 5 x 9.8 N.

To Find: Speed of the object = ?, the maximum number of revolutions per minute = N =?

Solution:

In vertical circle maximum tension is at the lowermost point

Ans: Speed of object = 6.64 m/s and maximum number of revolutions = 126.7 r.p.m.

Answer 2

Answer:

The speed of the object is 6.64 m/s.

Explanation:

Given that,

Mass of the object m= 0.5 kg

Length of the string r = 0.5 m

Tension $T = m\times g=5\times9.8$

We know that,

The maximum tension at the lower point is

$T_{max}=\dfrac{mv^2}{r}+mg$

$T_{max}=m(\dfrac{v^2}{r}+g)$

$\dfrac{v^2}{r}+g=\dfrac{T_{max}}{m}$

$v^2=r(\dfrac{T_{max}}{m}-g)$

$v^2=0.5(\dfrac{5\times9.8}{0.5}-9.8)$

$v^2=44.1$

$v=\sqrt{44.1}$

$v= 6.64\ m/s$

Hence, The speed of the object is 6.64 m/s.