A body is projected up with a velocity equal to √(9 G M/8 R) , where M is the mass of the earth and R is the radius of the earth. The maximum distance it reaches from the centre of the earth is

Question

A body is projected up with a velocity equal to √(9 G M/8 R) , where M is the mass of the earth and R is the radius of the earth. The maximum distance it reaches from the centre of the earth is (A) (10 R/9) (B) (16 R/7) (C) (10 R/3) (D) (9 R/8)

Tardigrade Admin · Accepted Answer

Let us assume that the maximum distance of the body from the centre of the earth is

h

.
Applying the conservation of mechanical energy, we get

\frac{1}{2} m (\frac{9 GM}{8 R})^{2} - \frac{GM m}{R} = - \frac{GM m}{h}

- \frac{7}{16} \frac{GM m}{R} = - \frac{GM m}{h}

\Rightarrow h = \frac{16 R}{7}

Q. A body is projected up with a velocity equal to $\frac{9 GM}{8 R}$ , where $M$ is the mass of the earth and $R$ is the radius of the earth. The maximum distance it reaches from the centre of the earth is

$\frac{10 R}{9}$

$\frac{16 R}{7}$

$\frac{10 R}{3}$

$\frac{9 R}{8}$

Q. A body is projected up with a velocity equal to 8R9GM​​ , where M is the mass of the earth and R is the radius of the earth. The maximum distance it reaches from the centre of the earth is

910R​

716R​

310R​

89R​

Let us assume that the maximum distance of the body from the centre of the earth is h . Applying the conservation of mechanical energy, we get 21​m(8R9GM​​)2−RGMm​=−hGMm​ −167​RGMm​=−hGMm​ ⇒h=716R​

Q. A body is projected up with a velocity equal to $\frac{9 GM}{8 R}$ , where $M$ is the mass of the earth and $R$ is the radius of the earth. The maximum distance it reaches from the centre of the earth is

$\frac{10 R}{9}$

$\frac{16 R}{7}$

$\frac{10 R}{3}$

$\frac{9 R}{8}$