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 RLet 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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