1.

The escape velocity for a planet is `v_(e)`. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will beA. `v_(e)`B. `(v_(e))/(sqrt(2))`C. `(v_(e))/2`D. zero

Answer» Correct Answer - b
From energy conservation
Potential inside sphere `V=-(GM)/(2R^(3))(3R^(2)-r^(2))`
`V_(S)=-(GM)/R,V_(0)=-(3GM)/(2R)`
Loss of potential energy of particle =Gain of kinetic energy
`m(V_(S)-V_(0))=1/2mv^(2)`
`v^(2)=2[-(GM)/R-(-(3GM)/(2R))]impliesv=sqrt((GM)/R)`
`v=sqrt((2GM)/R)impliesv=(V_(e))/(sqrt(2))`


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