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Question

An object projected vertically up from the earth's surface with velocity gR, where R is the radius of the earth and g is the acceleration due to gravity on the surface of earth. Find the maximum height reached by the object.

A
R
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B
2R
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C
R/2
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D
R/4
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Solution

The correct option is A R
Let the mass of the object be m and the maximum height reached be h.

Since external and non-conservative force are absent, so mechanical energy of the system will be conserved.


mechanical energy at earth surface = mechanical energy at highest point

Ui+KEi=Uf+KEf

GMmR+12m(gR)2=GMm(R+h)+0

at the highest point speed will be zero hence KEf=0

GMmR+12mgR=GMmR+h

Since, g=GMR2

GMmR+12mGMR=GMmR+h

12R=1R+h

h=R

Hence, option (a) is correct.
Why this question: To familiarize students with the application of conservation of mechanical energy, which is a core concept of this chapter.

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