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  • A spherical hole of radius is excavated from the asteroid of mass <img alt="\mathrm{M}" s

A spherical hole of radius \mathrm{R / 2} is excavated from the asteroid of mass \mathrm{M} as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is


 

Option: 1

\mathrm{\frac{G M}{R^2}}

 


Option: 2

\mathrm{\frac{G M}{2 R^2}}
 


Option: 3

\mathrm{\frac{G M}{8 R^2}}
 


Option: 4

\mathrm{\frac{7 G M}{8 R^2}}


Answers (1)

best_answer

\mathrm{ g_{\text {net }}= g_1-g_2 }

\mathrm{ g_1=\text { gravitational attraction due to sphere of radius } R }

\mathrm{ g_2=\text { gravitational attraction due to hollow sphere of radius } R / 2 \text { at surface. } }

\mathrm{ =\frac{G M}{R^2}-\frac{G\left[\frac{M}{(4 / 3) \pi R^3}\right] \frac{4}{3} \pi\left(\frac{R}{2}\right)^3}{(R / 2)^2}=\frac{G M}{2 R^2}}

Hence option 2 is correct.


 

Posted by

Ritika Harsh

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