Question

What would be the fictitious (pseudo) acceleration of the body lying on the equator of Earth in the radial direction away from the earth's centre due to its rotation?
(A) ωRe
(B) ω²Re
(C) ωRe ²
(D) ω²Re ² Where ω = angular speed of earth, Re = radius of earth

Answer 1

Answer:

Option (B) is correct.

Explanation:

since whenever body is performing a rotational motion it experience a centripetal force which is

$F_{c} =\frac{mv^{2} }{R}$..................(1)

we know that

$F=ma_{c}$............................(2)

from (1) and (2)

$ma_{c} =\frac{mv^{2} }{R}$

so

$a_{c} =\frac{v^{2} }{R}$.....................(3)

we know the relation between linear and angular speed

v=Rω................................(4)

from (3) and (4) we get,

$a_{c} ={R\varpi^{2} }$

So the rquired option is (B).

Answer 2

Answer:

(B) $R_{e} w^{2}$

Explanation:

Centripetal acceleration $a_{c}$ = $\frac{V^{2}}{R_{e}}$

but V = $R_{e}$ω

$a_{c}$ = $\frac{R_{e}^{2}w}{R_{e}}$ = $R_{e} w^{2}$