A body is projected vertically upwards from the surface of the earth. If its kinetic energy is equal to half of its minimum value required to escape f

Question

A body is projected vertically upwards from the surface of the earth. If its kinetic energy is equal to half of its minimum value required to escape f

A body is projected vertically upwards from the surface of the earth. If its kinetic energy is equal to half of its minimum value required to escape from the gravitational influece, then the height upto which it rises is
A. 4R
B. 3R
C. 2R
D. R

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

Correct Answer - D
Given K.E. `=(1)/(2)` (K.E.) escape
`=(1)/(2)((1)/(2)mv_(e)^(2))=(1)/(4)xx m((2GM)/(R ))=(GMm)/(2R)`
For upward motion, loss in K.E. = gain in P.E.
`therefore (GMm)/(2R)=-((GMm)/(R+h))-(-(GMm)/(R ))`
`therefore (1)/(2R)=(1)//(R )-(1)/(R+h)`
`therefore (1)/(R+h)=(1)/(2R)" " therefore h = R`

5 views Answered 2023-02-05 15:29