JEE Advanced · 2012 · 08 Apr 2012 · Paper 1 · Rotational Mechanics

A small mass

m

is attached to a massless string whose other end is fixed at

P

as shown in the figure. The mass is undergoing circular motion in the

x - y

plane with centre at

O

and constant angular speed

ω

. If the angular momentum of the system, calculated about

O

and

P

are denoted by

L_{O}

and

L_{P}

respectively, then

Answer: (C)

Solution

About

O

(the center of circular motion), the angular momentum

L_{O} = I ω

is constant in magnitude and direction (perpendicular to the plane). About

P

(off-center), the position vector from

P

to the mass changes direction as the mass rotates, so

L_{P} = r_{P} \times m v

varies with time. Therefore

L_{O}

remains constant while

L_{P}

varies.

JEE Advanced · 2012 · 08 Apr 2012 · Paper 1 · Single correct option