paper for gce a/l

7/24/2019 Paper for gce a/l

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Answer four questions only

(1)

(a)State the law of conservation of angularmomentum.

In a favorite classroom demonstration, a student holdsthe axle of a spinning bicycle wheel while seated on a

stool that is free to rotate (Fig. 11.1). !he studentand stool are initially at rest while the wheel isspinning in a hori"ontal plane with an initial angular

momentum #ithat points upward. $hen the wheel isinverted about its center by 1%&', the student and

stool start rotating. In terms of #i , what are themagnitude and the direction of # for the student plusstool

(b) student sits on a platform that is free to rotate on a frictionless bearing.!he angular velocity of the rotating platform is displayed on a computer. !hestudent rotates with a hand outstretched at &.*& m from the axis of rotationas shown in Figure +.

!he moment of inertia of the student and rotating platform is +.1gm-. !he

angular velocity is -. rad s1

.(i) /alculate the angular momentum of the student and rotating platform.

(ii) s the student rotates, she grasps a -.0 g mass from a stand as shownin Figure +./alculate the angular velocity of the student and platform 2ust after the mass

has been grasped.

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(iii) !he student then pulls the mass towards her body.7xplain the e8ect this has on the angular velocity of the student and theplatform

(c) In another investigation the student and platform rotate at 1.0 rad s 1. !hestudent puts one foot on the 9oor as shown in Figure +/.!he frictional force between the student:s shoe and the 9oor brings the

student and platform to rest in &.0 seconds. !he new moment of inertia ofthe student and platform is +.0gm-. /alculate the average frictional tor;ue

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2) A metal sphere of radius a contains a charge +Q and is surrounded by an uncharged,

concentric, metallic shell of inner radius b and outer radius c, as shown above. Express all

algebraic answers in terms of the given uantities and fundamental constants.

!a) "etermine the induced charge on each of the following and

explain your reasoning in each case.i. #he inner surface of the metallic shell

ii. #he outer surface of the metallic shell

!b) "etermine expressions for the magnitude of the electric field E as

a function of r, the distance from the center of the inner sphere, in

each of the following regions.

i. r $ aii. a $ r $ b

iii. b $ r $ c

iv. c $ r!c) %n the axes below, s&etch a graph of E as a function of r.


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5) As shown in 6igure 7(.0, water is pumped into a long vertical

cylinder at a rate of (. cm08s. #he radius of the cylinder is 5. cm,

and at the open top of the cylinder is a tuning for& vibrating with afreuency of 2 9:. As the water rises, how much time elapses

between

;uccessive resonances3! speed in air is 00m8s)

!b) 6or the arrangement shown in 6igure 7(./5, - 0 the inclined plane and the small pulleyare frictionless, the string supports the massM at the bottom of the plane, and the string has a

mass mthat is small compared withM. #he system is in euilibrium, and the vertical part of the

string has a length h. ;tanding waves are set up in the vertical section of the string. 6ind

!a) #he tension in the string

!b) #he whole length of the string !ignoring the radius of curvature of the pulley)

!c) #he mass per unit length of the string!d) #he speed of waves on the string

!e) #he lowestfreuency standing wave

!f) #he period of the standing wave having three nodes!g) #he wavelength of the standing wave having three nodes, and

!h) #he freuency of the beats resulting from the interference of the sound wave of lowest

freuency generated by the string with another sound wave having a freuency that is 2.

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