Question

A string length 1m is fixed at one end with a bob of mass 100g and the string makes ((2)/(pi))revs^(-1) around a vertical axis through a fixed point. The angle of inclination of the string with nvertical is

Answer 1

The angle of inclination with respect to vertical is cos⁻¹ (5/8).

The angle can be calculated as follows:

• As per the question,

Length of string = 1 m

Mass of bob = 100 g

ν = 2 / π ​rev/s

• Now, we know that, w=2πν

• Therefore,  w = 4 rad/s

• Also, mrw² = T sinθ where r = L sinθ, and mg =T cosθ,

• Thus, dividing  mrw²  and  mg we get,

        cos θ = g / w²​

                  = 10​ / ( 4 x 4 )

                  = 5 / 8

• Hence, ​ θ = cos⁻¹ (5/8)