Assuming earth as a uniform sphere of radius R, if we project a body along the smooth diametrical chute from the centre of earth with a speed v such that it will just reach the earth's surface then v is equal to

Question

Assuming earth as a uniform sphere of radius R, if we project a body along the smooth diametrical chute from the centre of earth with a speed v such that it will just reach the earth's surface then v is equal to (A) √g R (B) √2 g R (C) √(g R/2) (D) none of these

Tardigrade Admin · Accepted Answer

(K E+P E)1=(K E+P E)2 (1/2) m v2-(3/2) (G M m/R) =-(G M m/R) v=√(G M/R)=√(g R2/R) =√g R

Q. Assuming earth as a uniform sphere of radius $R$ , if we project a body along the smooth diametrical chute from the centre of earth with a speed $v$ such that it will just reach the earth's surface then $v$ is equal to

$g R$

$2 g R$

$\frac{g R}{2}$

none of these

$(K E + PE)_{1} = (K E + PE)_{2}$
$\frac{1}{2} m v^{2} - \frac{3}{2} \frac{GM m}{R}$
$= - \frac{GM m}{R}$
$v = \frac{GM}{R} = \frac{g R ^{2}}{R}$
$= g R$

Q. Assuming earth as a uniform sphere of radius R, if we project a body along the smooth diametrical chute from the centre of earth with a speed v such that it will just reach the earth's surface then v is equal to

gR​

2gR​

2gR​​