A tunnel is dug along a diameter of the planet. A particle is dropped into it at the surface. The particle reaches the centre of the planet with speed

Question

A tunnel is dug along a diameter of the planet. A particle is dropped into it at the surface. The particle reaches the centre of the planet with speed

A tunnel is dug along a diameter of the planet. A particle is dropped into it at the surface. The particle reaches the centre of the planet with speed v. If `v_(e)` is the escape velocity from the surface fo the planet, then-
A. `sqrt2v=v_(e)`
B. `v=v_(e)`
C. `v_(e)=sqrt3v`
D. `v_(e)=sqrt5v`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

`(1)/(2)mv^(2)=[-(GMm)/(R)]-[-(3GMm)/(2R)]`
or `(1)/(2)mv^(2)=(3GMm)/(2R)-(GMm)/(R)`
or `(v^(2))/(2)=(3GM)/(2R)-(GM)/(R)`
`(v^(2))/(2)=(GM)/(R)-(1)/(2)`
or `v=sqrt((GM)/(R))`
Also, `v_(e)=sqrt((2GM)/(R))=sqrt2v.`

5 views Answered 2023-02-05 15:29