Physics Times 07.2019

3.Sol:

0

16

3

Mg

x

k



2

(^2220)
(^004)
x
v x x   x 
(^0)
3 3 16 3 32
2 2 3 14
Mg K M
v x g
K M K
    
0
0 2 0
4
3 2
x 4 4 14 7
x x K g
a
M
   
8.Sol:
The rate of collision of the particle with the
piston is
1 v
2 /v 2L L

The speed of the particle after collision with
the piston is v 2 V
If the piston moves inward by dL the speed of
the particle increases by
v
v 2
2
dL
d V
V L
  
v
v
d dL
L
 
As^2
1 2 v 2
v
2 v
dK d dL
K m
K L

   
2
dK dL
K L

  

lnK 2ln lnL C

ln( ) lnKL C^2 

 KL^2 constant

 K Kf^4 i

Correct options are (a,c)

SECTION-2

1.Sol:

1 1 1

v u f

 

2 2 2

1 1 1

v u f

v u f

      

2 2 2

max

f v u

f v u

   

   

 

2

1 1

(20) 4(60 60) 4(30)(30)

f

 



where

1

4

   v u cm

5

36

 f

5 1

36 20

f

f



 

5 1 25

100% 100% %

36 20 36

f

f



    

0.69%

2.Sol: Momentum transferred to the mirror

2 Nh





(^) ( )
2
mean position
Nh
MV


V(mean position) A (where A m 1  )
2 Nh
M A

  (where 8 10 ^6 )
(10 )^6 8 10 10^66
2 2
M M
N
h h
     
 
12
4
10
M
N
h
  
 
N 1 10^12  x 1
8.Sol:
SECTION-2
1.Sol:
2.Sol:
3.Sol: