A boy has mass 80kg when resting on the ground at equator. what will be the centripetal acceleration on boy if radius of earth is 6.4×10 power 6 meter

0.338m-s^2

To calculate the centripetal acceleration of the boy, we need to use the following formula:

ac = ω^2 * r

where:
ac is the centripetal acceleration,
ω is the angular velocity, and
r is the radius.

Since the boy is at rest, the angular velocity is zero (ω = 0). Therefore, the centripetal acceleration would also be zero.

To calculate the centripetal acceleration on the boy, we can use the formula:

a = (v^2) / r

where:
a is the centripetal acceleration,
v is the velocity of the boy, and
r is the radius of the Earth.

To find the velocity of the boy, we need to calculate his speed at the equator. We know that the Earth rotates once every 24 hours, so the velocity of a point on the equator is given by:

v = (2πr) / t

where:
v is the velocity,
r is the radius of the Earth, and
t is the period of rotation (24 hours in this case).

Let's substitute the values into the formula:

v = (2π * 6.4×10^6) / (24 * 60 * 60)

First, we convert the time from hours to seconds (24 hours * 60 minutes * 60 seconds).

v = (2π * 6.4×10^6) / 86400

Now, we can calculate the velocity.

v ≈ 465.1 m/s

Next, substitute the values of velocity and radius of the Earth into the centripetal acceleration formula:

a = (465.1^2) / 6.4×10^6

a ≈ 3.36 m/s²

Therefore, the centripetal acceleration on the boy is approximately 3.36 m/s².