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CBSE Class 12-science Answered

a boa body is projected away from earth surface with a speed of a body at infinity if escape velocity is 15km /sec? ops: 32.33km /sec b. 42.42km /sec c. 31.45 km/sec d.40.42 km/sec
Asked by roopasreeallada14 | 25 May, 2024, 11:06: AM
answered-by-expert Expert Answer

It is understood that required velocity at infinity is 15 km/s, what is projeected velocity at earth's surface.

Let m be the mass of body .

Total energy Eo on earth surface is

img

Where first term of RHS is potential energy and second term is kinetic energy .

Where G is gravitational potential energy , M is mass of earth , m is mass of body , r is radius of earth and

vo is velocity of body on earth's surface.

At infinity , potential energy is zero and the body has only kinetic energy .

Hence energy at infinity is

img

where v is velocity at infinity.

By conservation of energy , 

Eo = E

img

if acceleration due to gravity  g = G (M/r2) , then above expression is simplifield for vo as

img

Let us substitute  g = 9.8 m/s2 , r = 6.371 × 106 m ,  v= 15 × 103 m/s in above expression to calculate vo .

we get vo = 18.70 m/s

 

 

 

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