2019-03-01_Physics_Times

With respect to trolley the velocity and

acceleration are

(10 2)^2

20 2

ar

  Since

2

r

g

a

 

  

 

2 2

 

    

 

LT LT T L

L

AY r Y Y r

2 

L

r

max for L = 100 cm & r = 0.2 mm

When the ball is just released, the net force on

ball is ma mg F  b

The terminal velocity ' 'vt of the ball is attained

when net force on the ball is zero.

mg F  b 6 rvt

When the ball acquires

2

3

rd of its maximum velocity

vf

2

' 6

3

t

b

v

ma mg F   r  

 

2

' ( )

3

ma ma  ma

'

3

a

a 

(^) [ ] ML T ^11
[ ]E ML T^2 ^2
[ ]^01
v M LTe
 
[ ] M L T^1 ^30
Moment of inertia of each of rod AC and BC
about the given axis OO’ is
2 2
(^260)
AC BC 3 4
m m
I  I sin 
 
and M.I of rod AB about the given axis OO’ is
2
(^332)
AB 2 4
I m m
 
    
 


Hence,
2 2
(^3252)
AC BC AB 4 4 4 4
m m
I I I I      m  m
 
 
Work done in stretching a string to obtain an
extension l is
1
1
2
W Kl
Similarly, work done in stretching a string to obtain
extension l 1 is
2
2 1
1
2
W  Kl
 Work done in second case
 
2 2
2 1 1
1
2
  W W K l l
As car is moving in anticlockwise direction
and have tangential acceleration as well as radial
acceleration. Friction component should be along
tangential and radial acceleration. The correct
option is (c).
The velocity of exhaust gases with respect to
rocket 100 ms^1
The minimum force on the rocket to lift it
Fmin mg 1000 10 10000  N
Hence, minimum rate of burning of fuel is given by
10.Sol:
11.Sol:
12.Sol:
13.Sol:
14.Sol:
15.Sol:
16.Sol:
17.Sol:
18.Sol:
min^100001001
r^100
dm F
kgs
dt u
   
From adiabatic relation between temperature
and volume
( 1) ( 1)
TVi i T Vf f
  