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) √gR (B) √2gR (C) √(gR/2) (D) none of these

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/6a4344ff8df9c40b36200875375f9fac-.png" /> (KE + PE)1 = (KE +PE)2 (1/2)mv2 - (3/2) (GMm/R) = -(GMm/R) v = √(GM/R) = √(gR2/R) = √gR

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​​