If the acceleration due to gravity at the earth’s surface is ( 9.8m/s2 ) and the mass of the earth is 80 times that of the moon and radius of earth 4 times that moon, the value of g at the moon’s surface will be ?

1 )  If the acceleration due to gravity at the earth’s surface is  ( 9.8m/s² ) and the mass of the earth is 80 times that of the moon and radius of earth 4 times that moon, the value of g at the moon’s surface will be ?

 A )   9.8m/s2   ,                                    B )   1.96 m/s2   ,

C )     4.9m/s2   ,                                   D )  None of these ,

Correct Answer : -       B )   1.96 m/s2   ,

Solution : -

Given Data : -

·         ge  = 9.8 m/s2        { ge = gravitational acceleration of earth }   ,

·         Me = 80 * Mm       { Me = mass of earth ,  Mm = mass of moon }  ,

·         Re = 4 * Rm         { Re  = Radius of earth ,  Rm = Radius of moon }  ,    

·         gm = ?   ,

Formula : -

ge = GMe / (Re)^2   ,

So , 

Ø   ge = G(80*Mm) / (4*Rm)^2

Ø   ge = (80)GMm / (16)(Rm)^2

Ø   ge = (5)GMm / (Rm)^2  ,

Ø   ge  = 5 * gm   ,

Ø   9.8 = 5 * gm   ,         (ge  = 9.8 m/s2 ) 

Ø    gm  = 9.8 / 5   ( m / s2 )   ,

Ø   gm = 1.96 m / s2   ,   Answer .

 

2 )  Centre of gravity is a point , where the whole ……………….. of body is to be centered .

A )  mass ,                                                  B ) weight ,

C ) Both of these ,                                                D ) None of these ,

Correct Answer : -   B ) weight ,

 

3 )  Find the velocity of pendulum in SHM which has amplitude of 0.2 m and time period of 0.01 sec ?

A ) 20 π ,                                           B ) 30 π , 

C ) 40 π ,                                           D ) None of these ,

Correct Answer ; -  C ) 40 π , 

Solution : -

Given Data : -

·         T = 0.01 s   ,

·         Xo = 0.2 m  ,

·         v = ?

Formula : -

v = r w   .

So first we have to find value of omega ( w )   ,   so

Ø  w = 2 π / T   ,

Ø  w = 2 π / (0.01)    ,

Ø  w = 200 π .

So  We simply put it formula : -

Ø  v = rw  ,

Ø  v = Xo * w    ,

Ø  v =  ( 0.2 ) * ( 200 π )  ,

Ø  v = 40 π  .  Answer

 

5 )   Centre of mass is a point , where the whole …………… of  body is to be  centered  .

A )  mass ,                                                  B ) weight ,

C ) Both of these ,                                                D ) None of these ,

Correct Answer : -  A )  mass ,       

 

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