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Introductory Exercise 7.3
1. | | v
1
®
= u and | | v
2
®
= v (say)
Dv v v
® ® ®
= + -
2 1
( )
       = -
® ®
v v
2 1
    D D v u u v v u
® ® ® ® ® ®
× = - × - ( ) ( )
2 1 2 1
         = × + ×
® ® ® ®
u v u v
2 2 1 1
 - -
® ®
2
2 1
v v
| | | | v v
2
2
1
2 2 2
® ®
+ = + v u
             = - + u gL u
2 2
2
       | | ( ) Dv
®
= -
2 2
2 u gL
         | | ( ) Dv
®
= - 2
2
u gL
2. Ball motion from A to B :
  0 2 2
2 2
= + - u g R
min
( )( )
Þ       u gR
min
2
4 =
Ball motion from C to A :
v u g h
2 2
2 = + -
min
( )
= - 4 2 gR gh 
Þ v g R h = - 2 2 ( )
3. Decrease in KE of bob
     = Increase in PE of bob
  
L
v
2
– v
1
Di
g
v
1
®
®
®
®
h
v
C
A
2R
B
PE of bob
= K (say)
KE of bob
2
= 1/2 mv
0
v
0
Page 3


            
          
 
          
Introductory Exercise 7.3
1. | | v
1
®
= u and | | v
2
®
= v (say)
Dv v v
® ® ®
= + -
2 1
( )
       = -
® ®
v v
2 1
    D D v u u v v u
® ® ® ® ® ®
× = - × - ( ) ( )
2 1 2 1
         = × + ×
® ® ® ®
u v u v
2 2 1 1
 - -
® ®
2
2 1
v v
| | | | v v
2
2
1
2 2 2
® ®
+ = + v u
             = - + u gL u
2 2
2
       | | ( ) Dv
®
= -
2 2
2 u gL
         | | ( ) Dv
®
= - 2
2
u gL
2. Ball motion from A to B :
  0 2 2
2 2
= + - u g R
min
( )( )
Þ       u gR
min
2
4 =
Ball motion from C to A :
v u g h
2 2
2 = + -
min
( )
= - 4 2 gR gh 
Þ v g R h = - 2 2 ( )
3. Decrease in KE of bob
     = Increase in PE of bob
  
L
v
2
– v
1
Di
g
v
1
®
®
®
®
h
v
C
A
2R
B
PE of bob
= K (say)
KE of bob
2
= 1/2 mv
0
v
0
  
1
2
0
2
mv mgh =
       v gh
0
2
2 =
       v gl
0
2 1 = - ( cos ) q
      = ´ ´ ´ - ° 2 5 1 60 9.8 ( cos )
         =7 ms
-1
        
      
          
      
  
       
 
          
           
         
        
       
          
  
 
  
          
      
        
   
   
h
PE of bob = K + mgh
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FAQs on DC Pandey Solutions: Circular Motion- 2 - DC Pandey Solutions for NEET Physics

1. What is circular motion?
Ans. Circular motion is the movement of an object along a circular path. In this type of motion, the object continuously changes its direction but maintains a constant distance from a fixed point called the center of the circle.
2. What is the difference between uniform circular motion and non-uniform circular motion?
Ans. In uniform circular motion, the speed of the object remains constant throughout the motion, while in non-uniform circular motion, the speed varies at different points along the circular path. In uniform circular motion, the object experiences a constant centripetal acceleration, whereas in non-uniform circular motion, the centripetal acceleration changes.
3. How is centripetal force related to circular motion?
Ans. Centripetal force is the force that acts towards the center of the circle, keeping an object in circular motion. It is responsible for continuously changing the direction of the object without changing its speed. The magnitude of the centripetal force can be calculated using the formula Fc = (mv^2)/r, where Fc is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the circular path.
4. What is the role of friction in circular motion?
Ans. Friction plays a crucial role in circular motion, especially when an object is moving on a curved surface. Friction provides the necessary centripetal force to keep the object in circular motion. It acts towards the center of the circle, opposing the outward force exerted by the object due to its inertia.
5. How is angular velocity different from linear velocity in circular motion?
Ans. Angular velocity refers to the rate of change of angular displacement of an object moving in a circular path. It is measured in radians per second. On the other hand, linear velocity refers to the rate of change of linear displacement of the object. Angular velocity depends on the radius of the circular path, while linear velocity depends on the distance traveled by the object.
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