a block of mass m is placed on a smooth turntable at a distance of 20cm from the centre.a string is tied to the block and its other end passed through a gole in the centre of the table.A 2nd block of mass m is suspended from the free end of the string as shown in fig.At what angular speed should turntable rotate so that the block placed on it should remain at rest on its surface?
tension max=mg from the hanging mass
centripetla force=mw^2*r
tensionmax=mr*w^2
mg=mr*w^2
w=sqrt(g/r) radians per second.
To find the angular speed at which the turntable should rotate so that the block placed on it remains at rest on its surface, we need to consider the forces acting on the system.
Let's analyze the forces acting on the suspended block (Block 2):
1. Tension in the string (T): It acts vertically upwards, supporting the weight of Block 2 (m * g).
Now, since Block 2 is at rest, the sum of all the forces acting on it should be zero in both the horizontal and vertical directions.
In the vertical direction:
T - m * g = 0
T = m * g
Since the tension in the string supports the weight of Block 2, it is equal to m * g.
In the horizontal direction, there are no external forces acting on Block 2.
Now, let's analyze the forces acting on the block placed on the turntable (Block 1):
1. Tension in the string (T): It acts horizontally, providing the required centripetal force for Block 1.
In order for Block 1 to remain at rest on the turntable, the centripetal force provided by the tension in the string should exactly counterbalance the centrifugal force acting on Block 1 due to its distance from the center of rotation.
The centripetal force (Fc) is given by the equation:
Fc = m * (v^2 / r)
Where,
m is the mass of Block 1,
v is the tangential speed of Block 1, and
r is the distance of Block 1 from the center of rotation.
In this case, as Block 1 is at rest, the tangential speed (v) is zero.
Therefore, the centripetal force required is also zero:
Fc = 0
In order for Block 1 to remain at rest, the tension in the string should also be zero in the horizontal direction.
Therefore, Block 1 will remain at rest on the turntable for any angular speed (angular velocity), as long as there is no external horizontal force acting on it.
Hence, there is no specific angular speed at which the turntable should rotate for the block to remain at rest on its surface.