A stone tied to a strong is made tn resolue in a horizontal circle of radius 4m with angular speed of 2 radian,persecond with what tingential velocity will the stone move off the circle if the string cuts
The tangential velocity will be the same as the value just before the string is cut:
(Radius)*(Angular Velocity) = 4 * 2 = 8 m/s
Tangential velocity=radius of circle -:- angular speed=4-:-2=2m/s
16N
To find the tangential velocity at which the stone will move off the circle when the string is cut, we can use the concept of centripetal force.
First, let's understand the situation. The stone is tied to a string and is moving in a horizontal circle of radius 4m with an angular speed of 2 radians per second. When the string is cut, the stone will continue to move in a straight line tangent to the circle until another force acts on it.
The centripetal force keeping the stone in circular motion is provided by the tension in the string. It is given by the formula:
F = m * (v^2 / r)
where F is the centripetal force, m is the mass of the stone, v is the tangential velocity, and r is the radius of the circle.
In this case, we need to find the tangential velocity at which the stone will move off the circle when the string is cut. Since the tension in the string will become zero when the string is cut, the centripetal force will also become zero.
Setting F = 0 in the formula, we have:
0 = m * (v^2 / r)
Simplifying the equation, we get:
v^2 = 0
Taking the square root of both sides, we have:
v = 0
Therefore, the tangential velocity at which the stone will move off the circle when the string is cut is zero.