JEE Main & Advanced Physics Gravitation Gravitational Field Intensity for Different Bodies

Gravitational Field Intensity for Different Bodies

Category : JEE Main & Advanced

(1) Intensity due to uniform solid sphere  

 

Outside the surface r > R On the surface r = R Inside the surface r < R
\[I=\frac{GM}{{{r}^{2}}}\] \[I=\frac{GM}{{{R}^{2}}}\] \[I=\frac{GMr}{{{R}^{3}}}\]

 

(2) Intensity due to spherical shell  

 

Outside the surface r > R On the surface r = R Inside the surface r < R
\[I=\frac{GM}{{{r}^{2}}}\] \[I=\frac{GM}{{{R}^{2}}}\] I = 0

 

(3) Intensity due to uniform circular ring

               

At a point on its axis At the centre of the ring
\[I=\frac{GMr}{{{({{a}^{2}}+{{r}^{2}})}^{3/2}}}\] I = 0

 

(4) Intensity due to uniform disc  

               

At a point on its axis At the centre of the disc
\[GM=g{{R}^{2}}\] or \[I=\frac{2GM}{{{a}^{2}}}\ (1-\cos \theta )\] I = 0

 


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