Suppose a vertical tunnel is dug along the diameter of the earth assumed to be a sphere of uniform mass having density ρ . If a body of mass m is thrown in this tunnel, its acceleration at a distance y from centre is given by,

Question

Suppose a vertical tunnel is dug along the diameter of the earth assumed to be a sphere of uniform mass having density ρ . If a body of mass m is thrown in this tunnel, its acceleration at a distance y from centre is given by, <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-rzkubn7zsp0tbg6m.jpg" /> (A) (4 π /3)gρ y (B) (3/4)π Gρ y (C) (4/3)π ρ y (D) (4/3)π Gρ y

Tardigrade Admin · Accepted Answer

Mass of the sphere is given by, M=(4/3)π y3ρ , gravitational force, F=(G ((4/3) π y3 ρ ) m/y2) a=(F/m) a=(G ((4/3) π y3 ρ ) m/y2 m)=(4/3)π Gρ y .

Q. Suppose a vertical tunnel is dug along the diameter of the earth assumed to be a sphere of uniform mass having density $ρ$ . If a body of mass $m$ is thrown in this tunnel, its acceleration at a distance $y$ from centre is given by,

$\frac{4 π}{3} g ρ y$

$\frac{3}{4} π Gρ y$

$\frac{4}{3} π ρ y$

$\frac{4}{3} π Gρ y$

Mass of the sphere is given by, $M = \frac{4}{3} π y^{3} ρ$ ,
gravitational force, $F = \frac{G ( \frac{4}{3} π y ^{3} ρ ) m}{y ^{2}}$
$a = \frac{F}{m}$
$a = \frac{G ( \frac{4}{3} π y ^{3} ρ ) m}{y ^{2} m} = \frac{4}{3} π Gρ y$ .

Q. Suppose a vertical tunnel is dug along the diameter of the earth assumed to be a sphere of uniform mass having density ρ . If a body of mass m is thrown in this tunnel, its acceleration at a distance y from centre is given by,

34π​gρy

43​πGρy

34​πρy

34​πGρy