A stone of mass 50g is being rotated in a circle of radius of 50cm with a uniform speed of 2 m/s. What is the acceleration of the stone??
To find the acceleration of the stone, we first need to understand the concept of centripetal acceleration.
Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It is always directed towards the center of the circle and is given by the formula:
a = (v^2) / r
Where:
a = centripetal acceleration
v = velocity of the object
r = radius of the circular path
In this case, we are given the mass of the stone (50g) and the speed at which it is rotating (2 m/s). However, we need to convert the mass to kilograms (as the SI unit for mass is kg) before we can proceed further.
1 kg = 1000 g
So, the mass of the stone in kilograms is: 50g / 1000 = 0.05 kg
Next, we need to convert the radius from centimeters to meters, as the SI unit for the radius is meters.
1 m = 100 cm
So, the radius of the circular path in meters is: 50 cm / 100 = 0.5 m
Now we have all the necessary values to calculate the acceleration.
Given:
Mass (m) = 0.05 kg
Speed (v) = 2 m/s
Radius (r) = 0.5 m
Using the formula for centripetal acceleration:
a = (v^2) / r
Plugging in the values:
a = (2^2) / 0.5
Simplifying:
a = 4 / 0.5
a = 8 m/s^2
Therefore, the acceleration of the stone is 8 m/s^2.