Physics Times 07.2019

(Kiana) #1

  1. An impulse J is exerted on a rod of mass m and
    length L at a distance x from the C.M. Find the
    value of x at which the net velocity of point P is
    zero.

  2. A cockroach of mass m is moving on the rim of a
    disc with velocity v in the anticlockwise direction.
    The moment of inertia of the disc about its own
    axis is I and it is rotating in the clockwise direction
    with angular speed


(a)

L
12

(b)

L
8 (c)

L
3 (d)

L
6

. If the cockroach stops
moving then the angular speed of the disc will be

(a)

I mvR
I


(b) 2

I mvR
I mR



(c) 2

I mvR
I mR



(d) 2

I
I mR





  1. The two uniform discs rotate separately on parallel
    axles. The upper disc (radius a and momentum of
    inertia










I 1 ) is given an angular velocity  0 and the
lower disc of (radius b and momentum of inertia
I 2 ) is at rest. Now the two discs are moved together
so that their rims touch. Final angular velocity of
the upper disc is

(a)

 
 

1 0
2 2
1 2 /

I
I a I b


   (b)

 
 

1 0
2 2
1 2 /

I
I b I a


  

(c)

 
 

2 0
2 2
2 1 /

I
I b I a


   (d)

 
 

2 0
2 2
2 1 /

I
I a I b


  


  1. c 2. d 3. c 4. a 5. a

  2. d 7. c 8. a






























1.Sol: Let l is the length of the rod.

2.Sol: Let v be the velocity of COM of ring just after
the impulse is applied and v’ its velocity when pure
rolling starts. Angular velocity

2

v J
m


2 2

2 2 2

l l l
J m m 
      
       
      

J
ml



(^) A 2 2 2
l J J J
v v
m m m
     
 of the ring at
this instant will be
v'
r
.
From impulse = change in linear momentum, we
have
J = mv v = J/m
Between the two positions shown in the figure,
force of friction on the ring acts backwards.
Angular momentum of the ring about bottom most
point will remain conserved
 L Li f
(^) mvr mv r I ' 
mv r mr v r mv r' ^2  '/  2 '
' 2 2
v v J
m
 
3.Sol: Impulse provided by the edge in the horizontal
direction:
1.Sol:
2.Sol:
3.Sol:

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