A body of mass 400g is
whirled in a vertical of radius 2m
at a steady rate of 2rev/s. find its
centripetal force.
A. 160N
B. 102N
C. 320N
D. 252N
The centripetal force can be found using the equation:
Centripetal force = mass * (velocity^2) / radius
First, we need to convert the mass to kilograms, so 400g = 0.4kg.
The radius is given as 2m.
The velocity can be calculated using the formula for the circumference of a circle:
Circumference = 2 * π * radius
The time for 1 revolution is 1/2s, since the body is whirled at a steady rate of 2rev/s.
Therefore, the velocity is:
Velocity = Circumference / Time
= 2 * π * radius / (1/2)
= 4 * π * radius
= 4 * 3.14 * 2
= 25.12m/s
Now we can calculate the centripetal force:
Centripetal force = 0.4kg * (25.12m/s)^2 / 2m
= 0.4kg * 630.2144m^2/s^2 / 2m
= 252.08576N
Therefore, the centripetal force is approximately 252N.
So, the answer is D. 252N.
To find the centripetal force, we can use the equation:
F = (m * v^2) / 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
In this case, we have:
- m = 400g = 0.4kg (converting grams to kilograms)
- v = 2rev/s
- r = 2m
First, let's calculate the velocity by converting the revolutions per second to meters per second.
To convert revolutions to meters, we need to find the circumference of the circular path:
C = 2πr
Where:
- C is the circumference
- π is a constant approximately equal to 3.14159
- r is the radius of the circular path
Substituting the values, we have:
C = 2π * 2m
C ≈ 12.57m
The velocity can be calculated by multiplying the circumference by the number of revolutions per second:
v = C * rev/s
v = 12.57m * 2rev/s
v ≈ 25.14m/s
Now, let's calculate the centripetal force using the equation:
F = (m * v^2) / r
F = (0.4kg * (25.14m/s)^2) / 2m
F = (0.4kg * 631.44m^2/s^2) / 2m
F = (252.576 N) / 2
F ≈ 126.288 N
Therefore, the centripetal force is approximately 126.288 N.
None of the given options match this value exactly.