question_answer

A bob of mass m attached to an inextensible string of length \[l\] is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed co rad/s about the vertical line passing through support. About the point of suspension,

A)  angular momentum is conserved

B)  angular momentum changes in magnitude but not in direction.

C)  angular momentum changes in direction but not in magnitude.

D)  angular momentum changes both in direction and magnitude.

Correct Answer: C

Solution :

Angular momentum of the pendulum about the suspension point O is: Then, can be resolved into two components, radial component \[{{v}_{rad}}\] and tangential component         \[{{v}_{\tan }}\] due to \[{{v}_{rad}},\] L will be tangential and due to \[{{v}_{\tan }},\,L\] will be the radically outwards as shown above. So, net angular momentum will be as shown in figure, So whose magnitude will be constant (|L| = mvl). But its direction will change as shown in the figure. \[L=m(r\times v)\] where r = position of particle from point 0. Method 2. Since torque about point of suspension due to mg of the conical pendulum is non zero and acting perpendicular to the angular momentum of pendulam about the point hence angular momentum changes in direction but not in magnitude.