a stone of mass 50g is being rotated in a circle of radius 50 cm with a uniform speed of 2 m/s what is the acceleration of the stone ?
Please tell solution
To find the acceleration of the stone, we need to first understand the concepts of circular motion. In circular motion, there are two types of acceleration: centripetal acceleration and tangential acceleration.
1. Centripetal acceleration (ac):
Centripetal acceleration is the acceleration towards the center of the circle. It is responsible for keeping an object moving in a circular path and can be calculated using the equation:
ac = (v^2) / r
where ac is the centripetal acceleration, v is the velocity, and r is the radius.
2. Tangential acceleration (at):
Tangential acceleration is the acceleration along the tangent to the circular path. It represents the change in magnitude of velocity. However, in this problem, the stone is rotating at a uniform speed, which means the tangential acceleration is zero.
Now let's calculate the centripetal acceleration:
Given:
Mass of the stone (m) = 50g = 0.05 kg
Radius (r) = 50 cm = 0.5 meters
Velocity (v) = 2 m/s
Using the formula:
ac = (v^2) / r
Substituting the given values:
ac = (2^2) / 0.5
Simplifying the equation:
ac = 4 / 0.5
ac = 8 m/s^2
Therefore, the acceleration of the stone is 8 m/s^2.