IIT-JEE 2012 · Paper 1 · Physics Q7

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PhysicsSingle correct+3 / -1Question 7 of 60

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 $\omega$ . If the angular momentum of the system, calculated about $O$ and $P$ are denoted by $\vec L_O$ and $\vec L_P$ respectively, then

A conical pendulum: string fixed at P on the vertical z-axis; the mass m moves on a horizontal circle (dashed) centred at O below P with angular speed ω.

\vec L_O

and

\vec L_P

do not vary with time.

\vec L_O

varies with time while

\vec L_P

remains constant.

\vec L_O

remains constant while

\vec L_P

varies with time.

\vec L_O

and

\vec L_P

both vary with time.

Answer and worked solution

Official answer: C

About O (the centre of the circle): $\vec L_O=m\vec r\times\vec v$ with $\vec r$ and $\vec v$ in the horizontal plane. It is $mr^2\omega\hat z$ , fixed in magnitude and direction.

About P (above the plane): the position vector from P has a vertical part, so $\vec L_P$ has a constant vertical component and a horizontal component that rotates with the mass. Its direction changes continuously.

(C)

Topics:Angular momentum and its conservation Circular motion dynamics

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IIT-JEE 2012 · Paper 1, Physics question 7