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Q: 8.2  Choose the correct alternative :

(a) Acceleration due to gravity increases/decreases with increasing altitude.     

(b) Acceleration due to gravity increases/decreases with increasing depth (assume the earth to be  a sphere of uniform density).              (c) Acceleration due to gravity is independent of mass of the earth/mass of the body.                                       

(d) The formula -GMm(1/r_2\hspace{1mm}-\hspace{1mm}1/r_1)  is more/less accurate than the formula mg(r_2-r_1) for the difference of potential energy                                   between two points r_2 and r_1  distance away from the centre of the earth. 

Answers (1)

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(a) Acceleration due to gravity decreases with increasing altitude.

       The relation between the two is given by :

                                               g_h\ =\ \left ( 1\ -\ \frac{2h}{R_e} \right )g

(b) Acceleration due to gravity decreases with increasing depth.

                              The relation is given below:

                                              g_d\ =\ \left ( 1\ -\ \frac{d}{R_e} \right )g

(c)  Acceleration due to gravity is independent of the mass of the body.                                       

                              g\ =\ \frac{GM}{R^2}                               Here M is the mass of the earth.

(d)  The formula -GMm(1/r_2\hspace{1mm}-\hspace{1mm}1/r_1)  is more accurate than the formula mg(r_2-r_1) for the difference of potential energy between two points r_2 and r_1  distance away from the centre of the earth. 

Posted by

Devendra Khairwa

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