A body is projected vertically upwards with a speed of √(G M/R) ( M is mass and R is radius of earth). The body will attain a height of

Question

A body is projected vertically upwards with a speed of √(G M/R) ( M is mass and R is radius of earth). The body will attain a height of (A) (R/2) (B) R (C) (5/4) R (D) (3 R/2)

Tardigrade Admin · Accepted Answer

Conserving mechanical energy at earth surface and at the maximum height attained by the body,

P . E_{i} + K . E_{i} = P . E_{j} + K . E_{j}

- \frac{GM m}{R} + \frac{1}{2} m (\frac{GM}{R}) = - \frac{GM m}{r} + 0

\Rightarrow - \frac{GM m}{2 R} = - \frac{GM m}{r}

\Rightarrow r = 2 R

\Rightarrow R + h = 2 R

h = R

Q. A body is projected vertically upwards with a speed of $\frac{GM}{R}$ ( $M$ is mass and $R$ is radius of earth). The body will attain a height of

$\frac{R}{2}$

$R$

$\frac{5}{4} R$

$\frac{3 R}{2}$

Q. A body is projected vertically upwards with a speed of RGM​​ ( M is mass and R is radius of earth). The body will attain a height of

2R​

R

45​R

23R​

Conserving mechanical energy at earth surface and at the maximum height attained by the body, P.Ei​+K.Ei​=P.Ej​+K.Ej​ −RGMm​+21​m(RGM​)=−rGMm​+0 ⇒−2RGMm​=−rGMm​ ⇒r=2R ⇒R+h=2R h=R

Q. A body is projected vertically upwards with a speed of $\frac{GM}{R}$ ( $M$ is mass and $R$ is radius of earth). The body will attain a height of

$\frac{R}{2}$

$R$

$\frac{5}{4} R$

$\frac{3 R}{2}$