Question

A 1 kg mass tied at the end of the string 0.5m long is whirled in a horizontal circle, the other end of the string being fixed. The breaking tension in the string is 50N. Find the greatest speed that can be given to the mass​

Answer 1

Answer:

Mass of the stone, m=0.25 kg

Radius of the circle, r=1.5 m

Number of revolution per second, n=40/60=2/3rps

Angular velocity, ω=2πn

The centripetal force for the stone is provided by the tension T, in the string, i.e.,

T=mω

2

r

=0.25×1.5×(2×3.14×(2/3))

2

=6.57 N

Maximum tension in the string, T

max

=200 N

T

m

ax=

r

mv

max

2

v

max

=(

m

T

max

r

)

1/2

=(200× 1.5/0.25)

1/2

=(1200)

1/2

= 34.64 m/s

Therefore, the maximum speed of the stone is 34.64 m/s.