Radius of moon = R

C

A vA

h

R

100

R

B

Mass= M

Moon

vB

Speed of particle at B = vB

Escape velocity on

surface of moon = ve

∴ v GM

e R

=^2

At highest point vA = 0

Mechanical energy is conserved in the process.

Decrease in kinetic energy =^1

2

mv^2

B

Increase in PE = UA – UB

VAGM

A Rh

= Potential at =

( + )

−

VBGM

R

B =Potential at = 1.5^ RR 0.5 R

(^3100)
2
2
−− − 

















= 3

2

1

2

99

(^3100)
2 2
−−  

















GM

R

RR

−− GM −

R

RGM

(^3) R
2
×
2
[3 0.98]= × 2.02
2
∴−Increase in PE =

• 
  


• 
  

  × (1.01)
  GMm
  Rh
  GMm
  R
  Equate KE and PE.
  1
  2

  
  

  ( + )
  mv^2 GMm +^ × 1.01
  Rh
  GMm
  B R
  −
  GM
  R
  GM
  Rh R
  = 1

  
  


• 
  

− + 1.01







or^1 =^1

+

+ 1.01

RRhR

−

or^1

+

= 0.01 = 1

Rh RR (^100)
or 100 R = R + h or h = 99R

7. (a) : Let R be the radius of circular layer of water.
   en pR^2 dρ = m

d

A

T

Pressure at AP

T

d

=− 0

2

(meniscus is cylindrical in

shape)

Pressure between the plates is less than the

atmospheric pressure and so the plates are pressed

together.

F = Force of attraction = 'ρ × area

F

T

d

=×R

(^22)
π

=×^22 T = 2

d

m

d

Tm

.ρ dρ

=

×××

××

=

−

−

20210007

00110 1000

28

3

(^24)

..

.

.N

8. (c)


9. (b) : Variation of acceleration due to gravity with
   altitude

gg h

h Re

=−







(^12) ; ∆g gh
Re

=

2

Variation of l with temperature = 'l

Linear expansivity = ∆

∆

l

l()θ

T l

gg

l

g

g

g

T g

h g

=

−

=−







=+







−

2211

2

12

ππ

∆

∆∆/

T ll

g

T l

θ l

21 π= + =+ 

2

∆∆

e clock shows correct time if Th = Tq , ∆

l ∆

l

g

22 g

=

Linear expansivity = ∆

l ∆

l

g

g

h

R

h

(^1010) eeR

2

10 5

===

National Talent Search Examination

The Schedule of NTSE-2018-19

Stage Area Tentative Dates

Stage-I

(State)

Last Date for Submission of

Application Form

To be notified by the

respective State/UT. May

vary from state to state.

Examination in Mizoram,

Meghalaya, Nagaland and

Andaman and Nicobar Islands

03 th November, 2018

(Saturday)

Examination in All other

States and Union Territories

04 th November, 2018

(Sunday)

West Bengal^18

th November, 2018

(Sunday)

Stage-II

(National)

Examination in All States and

Union Territories^12

th May, 2019 (Sunday)