Question

mass is whirled in a circular path with constant angular velocity and its linear velocity is v. If the string is now halved keeping the angular momentum same, the linear velocity is ______.

Options

• 2v

• `"v"/2`

• v

• `"v"sqrt2`

Answer 1

mass is whirled in a circular path with constant angular velocity and its linear velocity is v. If the string is now halved keeping the angular momentum same, the linear velocity is 2v.

Explanation:

Angular velocity = ω

Linear velocity = v

Length of string = Radius = r

If string is halved, r' = `"r"/2`

Angular momentum, L = r × p

where, r = radius vector

and p = linear momentum.

= r × mv     ....[∵ θ = 90°]

= mvr

As L remain constant,

mvr = constant

`=> "If" "r'" -> "r"/2`, n' = 2v such that

m v' r' = `"m 2 v" xx "r"/2`

= m v r

Hence, linear velocity will be 2 v.