A stone of mass m tied to a rope is rotated in a vertical circular path of radius r with uniform speed v. The total downward forces acted on the stone at the lowest point is:

Correct option is D

To provide this centripetal force at the lowest point, the rope must exert a tension force that overcomes both the weight of the stone and supplies the centripetal force.

So, the net downward force that must be balanced by the rope’s tension is:

T =$$\frac{mv^2}{r} + mg$$

mg is constant and represents weight of the object.

mv²/r is derived from Newton’s second law applied to circular motion.​​

• The gravitational force (mg) is always acting downward, regardless of the position of the stone in its circular path.

• Centripetal force (mv²/r)– Required to keep the stone moving in a circular path, also directed towards the center, which is upward from the stone's perspective, but must be provided by the tension in the rope.