A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now the platform is given an angular velocity `omega_(0)`. When the tortoise move along a chord of the platform with a constant velocity (with respect to the platform),

Options

A.
B.
C.
D.

Answer

B

Explanation

Since, there is no external torque, angular momentum will remain conserved. The momentum will remain conserved. The moment of inertia will first decreases till the tortise moves from `A` to `C` and then increases as it moves from `A` to `C` and then increases as it moves from `C` to `D`. Therefore,`omega` will initially increases and then decrease. Let `R` be the radius of platform, `m` the mass of disc and `M` is the mass of platform.
moment of inertia when the tortoise is at `A`
`I_(1) = mR^(2) + (MR^(2))/(2)`
and moment of inertia when the torroise is at `B`

`I_(2) = mr^(2) + (MR^(2))/(2)`
here, `r^(2) = a^(2) + [ sqrt(R^(2) - a^(2)) - vt]^(2)`
From conservation of angular momentum
`omega_(0) I_(1) = omega(t) I_(2)`
Sustituting the values we can see the variation of `omega (t)` is non-linear.