Question

A particle of mass m is tied to a string of length l and whirled into a horizontal plane.If tention in the string is t then the circular speed of the particle will be

Answer 1

T = tension force in the string

m = mass of the particle

v = circular speed of the particle

r = radius of the circular path traveled by the particle = l

F = centripetal force

we know that centripetal force is given as

F = m v²/r  

The tension force here provides the necessary centripetal force for the particle to move in circle , hence

T = F

T = m v²/r  

since r = l

hence

T = m v²/l

multiplying both side by "l/m"

Tl/m = (m v²/l) (l/m)

v² = Tl/m

taking square root both side

√v² = √(Tl/m)

v = √(Tl/m)

Answer 2

Answer:

Question :

A particle of mass m is tied to a string of length l and whirled into a horizontal plane.If tention in the string is t then the circular speed of the particle will be

Given:

T = tension force in the string

m = mass of the particle

v = circular speed of the particle

r = radius of the circular path traveled by the particle = l

F = centripetal force

Solution :

we know that centripetal force is given as

F = m v²/r

The tension force here provides the necessary centripetal force for the particle to move in circle , hence

T = F

T = m v²/r

since r = l

hence

T = m v²/l

multiplying both side by "l/m"

Tl/m = (m v²/l) (l/m)

v² = Tl/m

taking square root both side

√v² = √(Tl/m)

v = √(Tl/m)

Answer : v = √(Tl/m)