A ball of mass 50 g tied to the end of a 50 cm inextensible string is whirled around in a vertical circle. Find the tension in the string when the ball is at the top of the circle. Take g=10m s2

tension=mv^2/r-mg So you have to know the velocity, tension depends on the velocity.

To find the tension in the string when the ball is at the top of the circle, we can consider the forces acting on the ball.

At the top of the circle, the ball is momentarily at rest, so the tension in the string provides the centripetal force required to keep the ball moving in a circular path.

The tension in the string can be determined using the following equation:

Tension = Centripetal force

The centripetal force can be found using the formula:

Centripetal force = (mass x velocity^2) / radius

Here, the mass of the ball is 50 g, which is equivalent to 0.05 kg. The radius of the circular path is given as 50 cm, which is equivalent to 0.50 m. Since the ball is at the top of the circle, its velocity is zero at that point.

Substituting these values into the formula, we have:

Centripetal force = (0.05 kg x 0^2) / 0.50 m

Since the velocity is zero, the centripetal force will also be zero.

Therefore, the tension in the string when the ball is at the top of the circle is zero.

To find the tension in the string when the ball is at the top of the circle, we need to consider the forces acting on the ball at that position.

At the top of the circle, the ball is moving in a circular path with a constant speed. The gravitational force acts vertically downward, and the tension in the string acts towards the center of the circle.

Since the ball is not accelerating horizontally (moving in a circular path with constant speed), the net force acting on the ball in the horizontal direction must be zero.

Let's consider the forces acting on the ball at the top of the circle:
1. Gravitational force (mg): The force due to gravity acting vertically downward is given by the mass of the ball multiplied by the acceleration due to gravity (g). In this case, the mass of the ball is 50 g (which is 0.05 kg) and the acceleration due to gravity is 10 m/s^2. So, the gravitational force is: F_gravity = (0.05 kg) x (10 m/s^2) = 0.5 N.

2. Tension in the string (T): The tension in the string acts towards the center of the circle and provides the necessary centripetal force to keep the ball moving in a circular path. At the top of the circle, the tension is acting upwards to balance the gravitational force. To find the tension, we need to equate the centripetal force to the total force acting in the vertical direction.

The centripetal force can be calculated using the formula: F_centripetal = (mass of the ball) x (velocity)^2 / (radius of the circle).

Since the ball is moving in a vertical circle, the velocity at the top of the circle can be found using the equation of motion: v^2 = u^2 + 2as, where u is the initial velocity (which is zero), a is the acceleration (which is the gravitational acceleration, g), and s is the displacement (which is equal to the radius of the circle, since the ball is at the top).

So, the velocity at the top of the circle is: v = sqrt(2gh), where h is the height of the circle (which is the radius of the circle).

In this case, the radius of the circle is given as 50 cm (which is 0.5 m). So, the velocity at the top of the circle is: v = sqrt(2 x 10 m/s^2 x 0.5 m) = sqrt(10) m/s.

Now, we can calculate the centripetal force: F_centripetal = (0.05 kg) x (sqrt(10) m/s)^2 / (0.5 m) = 1 N.

Since the net force in the vertical direction is zero at the top of the circle, the tension minus the gravitational force must equal the centripetal force. Therefore, T - F_gravity = F_centripetal.

Substituting the values, we have: T - 0.5 N = 1 N.
T = 1 N + 0.5 N = 1.5 N.

Therefore, the tension in the string when the ball is at the top of the circle is 1.5 N.