A body of mass 0.1 kg is being rotated in a circular path of diameter 1 m on a frictionless

horizontal plane by means of a string. It performs 10 revolutions in 31.4 sec, calculate the
centripetal force acting on the body

To calculate the centripetal force acting on the body, we need to use the formula for centripetal force:

F = (m * v²) / r

Where:
F is the centripetal force
m is the mass of the body
v is the velocity of the body
r is the radius of the circular path

First, let's find the velocity of the body. We can calculate this by using the formula for linear velocity:

v = (2 * π * r) / T

Where:
v is the velocity
r is the radius of the circular path
T is the time for one revolution

Given that the diameter of the circular path is 1m, we can calculate the radius (r) by dividing the diameter by 2:

r = 1m / 2 = 0.5m

Next, we can calculate the time for one revolution (T) by dividing the total time it takes for the body to perform 10 revolutions (31.4 sec) by 10:

T = 31.4 sec / 10 = 3.14 sec

Now we can substitute the values into the formula for velocity:

v = (2 * π * 0.5m) / 3.14 sec
v ≈ 1.00 m/s

Now that we have the velocity, we can substitute it into the formula for centripetal force:

F = (0.1 kg * (1.00 m/s)²) / 0.5m
F = 0.1 kg * 1.00 m²/s² / 0.5m
F = 0.1 kg * 1.00 m²/s² / 0.5m
F = 0.1 kg * 1.00 m/s²
F = 0.1 N

Therefore, the centripetal force acting on the body is 0.1 Newtons.

O.2N