A 3kg mass is attached to end of a light rod and made to move clockwise in a vertical circle of radius 2m and speed of 6m/s. The tension in the rod at the lowest point is most nearly
A. 54N
B. 84N
C. 30N
D. 24N
E. 39N
To find the tension in the rod at the lowest point, we need to consider the forces acting on the mass. At the lowest point of the vertical circle, the mass is moving in a circular path with the maximum speed, which means it is experiencing its maximum centripetal acceleration.
The centripetal force required to keep the mass moving in a circle is provided by the tension in the rod. This force is given by the equation:
Centripetal force = (mass) x (centripetal acceleration)
The centripetal acceleration, in this case, can be calculated using the formula:
Centripetal acceleration = (velocity^2) / (radius)
Given that the mass of the object is 3kg, the radius of the circle is 2m, and the speed is 6m/s, we can calculate the centripetal acceleration:
Centripetal acceleration = (6^2) / 2 = 36 / 2 = 18 m/s^2
Now we can calculate the centripetal force:
Centripetal force = (3kg) x (18m/s^2) = 54 N
Therefore, the tension in the rod at the lowest point is most nearly 54 N, which corresponds to option A.