Question

A body thrown vertically upward with initial speed sqrt (gR), where R is the radius of earth. Then maximum height reached by body from the surface of earth is

1) R/2
2) 3R/2
3) R
4) R/4

Answer 1

correct answer is R/2

Answer 2

The correct answer is option (c) R.

Given,

A body is thrown vertically upward with initial speed √(gR), where R is the radius of the earth.

To Find,

The maximum height reached by the body from the surface of the earth.

Solution,

The initial potential energy = Ui = -GMm/(R+h)

The final potential energy = Uf = -GMm/R

Now, using the law of conservation of energy

1/2mv² = -GMm/(R+h) + GMm/R

1/2m(√gR)² = -GMm/(R+h) + GMm/R

1/2mgR = -GMm/(R+h) + GMm/R

Substituting the value of g as GM/R²

1/2m(GM/R²)R = -GMm/(R+h) + GMm/R

1/2GMm/R-GMm/R = -GMm/(R+h)

-1/2GMm/R = -GMm/(R+h)

2R = R+h

R = h

Hence, the maximum height reached by the body from the surface of the earth is R.

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