Questions - Answers

Very short answers questions

1.  Out of mass and weight which is a variable?  Why?
A: Mass is quantity of matter contained in a body. While weight = mg. As weight depends on acceleration due to gravity which inturn depends on height, depth, latitude and shape of earth, so weight is a variable while mass is constant.
 

2.  What is the acceleration due to gravity and weight of body at centre.
A:  At a depth 'd' acceleration due to gravity g_d =  g 
     At centre d = R. Hence at centre gR = g  = 0
      weight = Mg_R = 0.   So both are zero at centre of earth.
 

3.  Why hydrogen is in abundance on sun when compared with that of earth's atmosphere?
A:  The r.m.s. velocity of H₂, N₂, O₂ molecules in earth is less than that of escape velocity of earth. While on sun the r.m.s. velocity of N₂, O₂ molecules is more than that of sun's escape velocity. So N₂, O₂ molecules will not be in sun's atmosphere and only hydrogen will be present.

4.   What is the relation between orbital velocity and escape velocity?  

Short Answer Questions
1.  Define an expression for orbital velocity and define it.

Sol:  The horizontal velocity required for an object to revolve around a planet in a circular orbit is called orbital velocity.
            Consider an object of mass 'm' revolve around a planet of mass 'M', radius 'R' at a height 'h'. Let its horizontal speed in the orbit be v_o.

                            
2.   Derive an expression for escape velocity.
Sol: The minimum vertical velocity required for an object to escape from gravitational influence of a planet is known as escape velocity v_e.  Consider an object of mass 'm' on a surface of a planet of radius 'R' and mass 'M'.
             Gravitational potential on the surface of planet  =  

                Gravitational potential energy of the object  =  

                    K.E. of the object  =   

3. Find the depth at which the value of g become 25% of that at the surface of the earth
    (R = 6400 km)