A tunnel is dug along the diameter of the earth. A mass m is dropped into it. How much time does it take to cross the earth?

Question

A tunnel is dug along the diameter of the earth. A mass m is dropped into it. How much time does it take to cross the earth? (A) 169.2 min (B) 84.6 min (C) 21.2 min (D) 42.3 min

Tardigrade Admin · Accepted Answer

Time period to cross the earth once along its diameter =(T/2) =(1/2)(2 π √(R/g)) =π √(R/g) Where, R is the radius of the earth =3.14× √(6.4 × 106/9.8)=2537.5 s =42.3 min

Q. A tunnel is dug along the diameter of the earth. A mass $m$ is dropped into it. How much time does it take to cross the earth?

$169.2 min$

$84.6 min$

$21.2 min$

$42.3 min$

Time period to cross the earth once along its diameter $= \frac{T}{2}$
$= \frac{1}{2} (2 π \frac{R}{g})$
$= π \frac{R}{g}$
Where, $R$ is the radius of the earth
$= 3.14 \times \frac{6.4 \times 1 0 ^{6}}{9.8} = 2537.5 s$
$= 42.3 min$

Q. A tunnel is dug along the diameter of the earth. A mass m is dropped into it. How much time does it take to cross the earth?

169.2min

84.6min

21.2min

42.3min