A small mass M attached to a string slides in a circle (x) on a frictionless hor

Question

A small mass M attached to a string slides in a circle (x) on a frictionless horizontal table, with the force F providing the necessary tension (see figure). The force is then increased slowly and then maintained constant when M travels around in circle (y). The radius of circle (x) is twice the radius of circle (y).

Options for answers are: True, False, Less than, Greater than, or equal to

1)M's angular momentum at x is .... that at y.
2)While going from x to y, there is a torque on M.
3)M's kinetic energy at x is one quarter that at y.
4)As M moves from x to y, the work done by F is .... 0.
5)M's angular velocity at y is four times that at x.

Explanation / Answer

1)

equal to

According to conservation of angular momentum

angular momentum at x = angular momentum at y

2)

False

since the Force F is not perpendicular to the radius, hence there is no net torque

3)

True

Using conservation of angular momentum

m vx rx = m vy ry

vx rx = vy ry

vx /vy = 0.5

KEx /KEy = (0.5) m vx2 /((0.5) m vx2 ) = (vx /vy )2 = (0.5)2 = 0.25

4)

Equal to

Since there is no net Torque , hence work done = 0

5)

False

angular velocity remains same

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