A body of mass 0.1kg is moving on circular path of diameter 1m at the rate of 10 revolution per 31.4sec, then then centripetal force acting on body is
A) 0.2N B) 0.4N
C)2N D) 4N
first get velocity tangent to circle v
it goes pi D meters in 3.14 seconds
v = pi D/3.14 = pi * 1/ 3.14 = 1 m/s
centripetal acceleration = Ac =v^2/R =1*1/.5
= 2 m/s^2
F = m Ac = .1 * 2 = .2 Newtons
To find the centripetal force acting on a body moving in a circular path, we need to use the formula:
Centripetal force (F) = (mass of the body) × (velocity squared) / (radius of the circular path)
Given:
- Mass of the body = 0.1 kg
- Diameter of the circular path = 1 m, which means the radius (r) of the circular path is 1/2 m
- Rate of revolution = 10 revolutions / 31.4 sec
First, let's find the velocity of the body.
The velocity of an object moving in a circle is given by the formula:
Velocity = (2πr) × (revolution per second)
In this case, the diameter is 1m, so the radius is 1/2 m. The rate of revolution is 10 revolutions in 31.4 seconds.
Velocity = (2π × 1/2) × (10 / 31.4) m/s
= (π / 31.4) m/s
Now, we can substitute the values into the centripetal force formula:
F = (mass of the body) × (velocity squared) / (radius of the circular path)
= 0.1 kg × [(π / 31.4) m/s]² / (1/2) m
= 0.1 kg × [(π / 31.4)²] / (1/2) m
To calculate this, we need the value of π (pi), which is approximately 3.14.
F = 0.1 kg × [(3.14 / 31.4)²] / (1/2) m
= 0.1 kg × (0.01) / (1/2) m
= 0.1 kg × 0.01 / (1/2) m
= 0.1 kg × 0.01 × (2/1) m
F = 0.2 N
Therefore, the centripetal force acting on the body is 0.2 Newtons.
Hence, the correct option is A) 0.2N.
To find the centripetal force acting on the body, we need to use the formula:
F = (m * v^2) / r
Where:
F = centripetal force
m = mass of the body
v = velocity of the body
r = radius of the circular path
Given:
m = 0.1 kg (mass of the body)
diameter = 1 m (diameter of the circular path)
radius (r) = diameter / 2 = 1m / 2 = 0.5m
To find the velocity (v), we can use the formula:
v = (2 * π * r * n) / t
Where:
n = number of revolutions
t = time taken for the given number of revolutions
Given:
n = 10 (number of revolutions)
t = 31.4 sec (time taken)
Substituting the values into the formula:
v = (2 * π * 0.5m * 10) / 31.4 sec
Now we can calculate the velocity (v):
v = 0.3185 m/s
Now we can substitute the values of mass (m), velocity (v), and radius (r) into the centripetal force formula:
F = (0.1 kg * (0.3185 m/s)^2) / 0.5 m
Simplifying the equation:
F = (0.03217 kg m^2/s^2) / 0.5 m
F = 0.06434 N
So, the centripetal force acting on the body is approximately 0.06434 N.
None of the given options (A, B, C, or D) match this value.