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Express escape velocity in terms of g, R...

Express escape velocity in terms of g, R and `rho` (the earth's density).

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Escape velocity, `v_("esc")=sqrt((2GM)/(R))`
The earth's density, `rho=("mass")/("volume")=(M)/(((4)/(3))piR^(3))`
`therefore M=(4)/(3)piR^(3)rho`
`therefore v_("esc")=sqrt((2G(4//3)piR^(3)rho)/(R))`
`=sqrt(2G(4//3)piR^(2)rho)=2R sqrt(((2)/(3)Gpi rho)`
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NAVNEET PUBLICATION - MAHARASHTRA BOARD-GRAVITATION -Answer the following questions :
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  8. Define free fall .

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  9. Explain the term free fall and state the corresponding kinematical equ...

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  12. What is gravitational potential energy?

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  13. Define gravitational potential energy. Write the formula for it.

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  16. Explain the term escape velocity.

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  17. Write a short note on escape velocity.

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  18. Using the law of conservation of energy, obtain the expression for the...

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  20. Express escape velocity in terms of g, R and rho (the earth's densit...

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