Question

The image shows the distances of points P and Q from the Earth’s center. If rQ>rP, how would the acceleration due to gravity (g) and weight of an object (W) compare at these two points

(a)gP>gQ and WP > WQ
(b)gP<gQand WP < WQ
(c)gP>gQand WP < WQ
(d)gP<gQand WP > WQ​

Answer 1

Answer:

Correct answer is c if you have

Answer 2

The comparison between g and W at these two points will be : (b)  $g_{P}$ < $g_{Q}$ and  $W_{P} <W_{Q}$

We know, the acceleration due to gravity at a depth of d from the surface of the earth is,

g' = g ( 1 - $\frac{d}{R}$)  

Where g = acceleration due to gravity on the surface of the earth

           R = Radius of the earth

Given, the depth from the point P = $r_{P}$  

           the depth from the point Q = $r_{Q}$

and,  $r_{Q}$ > $r_{P}$

So,

$g_{P}$ = g ( 1 - $\frac{r_{P} }{R}$)

$g_{Q}$ =  g ( 1 - $\frac{r_{Q} }{R}$)

As,  $r_{Q}$ > $r_{P}$,

∴  $\frac{r_{P} }{R}$ > $\frac{r_{Q} }{R}$

∴  1 - $\frac{r_{P} }{R}$ < 1 - $\frac{r_{Q} }{R}$

∴ $g_{P}$ < $g_{Q}$

∵ Weight of an object is = mass of the object × acceleration due to gravity of the point where it is measured,

∴ $W_{P} <W_{Q}$ , ∵ mass is constant as the object is same

∴ The comparison between g and W at these two points will be :

(b)  $g_{P}$ < $g_{Q}$ and  $W_{P} <W_{Q}$