Physics Times – July 2019

(c)y i x j^2 ˆ ˆ^2 (d) yi x jˆ ˆ^2

11. Verify whether the following forces are
    conservative or not.
    (1) F xyi xyj ˆ ˆ Ans : Non conservative

(2) F xi yj ˆ ˆ Ans : conservative

(3) 3

rˆ

F

r

 Ans : conservative

(4) F r r^2 ˆ Ans : conservative

(5) F Ci ˆ (C - is a constant)

Ans : conservative

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


2. b 7. a 8. b 9. d 10. a


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         4. 
            
            
            
            5. 
               
            
            
            
            
         
         
         
         
      
      
      
      
   
   
   
   


4. 
   
   
   
   7. 
      
      
      
      8. 
         
         
         
         9. 
            
            
            
            10. 
                
            
            
            
            
         
         
         
         
      
      
      
      
   
   
   
   

1.Sol: Positive work done by a conservative force
always decreases the potential energy
W U
    U (W) ( ve) ve
2.Sol: Among the given forces, force of friction
is a non-conservative force whereas all other
forces are conservative forces.
3.Sol: In case of non-conservative forces, the
work done is dissipated as heat, sound etc, i.e.,
it does not increase the potential energy.
4.Sol: Conceptual

5.Sol: (^) W U
6.Sol: Conceptual
7.Sol: Gravitational force is a conservative force
and work done against it does not depend on
the path.
8.Sol: Conceptual
9.Sol: Any constant force is a conservative force.
10.Sol: If the force
1.Sol:
2.Sol:
3.Sol:
4.Sol:
5.Sol:
6.Sol:
7.Sol:
8.Sol:
9.Sol:
10.Sol: F Fi F j x yˆ ˆ

is conservative
then
Fx Fy
y x
 

 
F xy i x y j ^2 ˆ^2 ˆ
(^2) , 2
F xy F x yx y
x  ^22
F
xy xy
y y
 
 
 
y   (^22)
F
x y xy
x x
 
 
 
Fx Fy
y x
 
 
 
F xyi xy j ˆ ˆ

F xy F xyx , y
x & y
F F
x y
y x
 
 
 
Fx Fy
y x
 
 
 
F y i x j ^2 ˆ ˆ^2
(^2) , 2
F y F xx y
x   (^22)
F
y y
y y
 
 
 
 ^22
Fy x x
x x
 
 
 
Fy Fx
x y
 

 
F yi x j ˆ ˆ^2
,^2
F y F xx y
x 1, y 2
F F
x
y x
 
 
 
Fx Fy
y x
 

 
So option (a) is correct.