a stone tied to a strong is made to revolve in a horizontal circle of radius 4 m with an angular speed of 2 radian per second. with what tangential velocity will the stone move off the circle if the string cuts?

Vt = omega * r = 2 * 4 = 8 m/s

4*2=8m/per second

234 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 acceleration.

The centripetal acceleration (ac) is given by the formula:

ac = r * ω^2

Where:
ac is the centripetal acceleration
r is the radius of the circular path
ω (omega) is the angular velocity

In this case, the radius (r) is given as 4 meters and the angular velocity (ω) is given as 2 rad/s. We can substitute these values into the formula to find the centripetal acceleration:

ac = 4 * (2^2)
ac = 4 * 4
ac = 16 m/s^2

Now, the moment the string is cut, the stone will move off the circle due to the absence of centripetal force. At this moment, the stone will continue moving tangentially with the velocity that was previously keeping it in the circular path.

The tangential velocity (vt) can be calculated using the formula:

vt = ac * t

Where:
vt is the tangential velocity
ac is the centripetal acceleration (calculated earlier as 16 m/s^2)
t is the time taken for the stone to move tangentially after the string is cut (which will be very small)

Since the time taken for the stone to move tangentially after the string is cut is very small, we can assume it to be negligible. Hence, the tangential velocity can be approximated to:

vt ≈ ac * 0

Since the time (t) is considered as zero, the tangential velocity will be zero.

Therefore, when the string is cut, the stone will move off the circle with a tangential velocity of zero.