Question

Object of mass 1 kg is tied to one end of a string of length 9 metre and whirled in a vertical circle what is the minimum speed required at the lowest position in a circle

Answer 1

mass of object (m) = 1 kg
length of string (R) = 9m
Let the speed of object at the lowest position = u
And highest position = V
at the lowest position,
T - mg = mu²/R
at the highest position ,
T + mg = mV²/R

and work energy theorem ,
1/mV² + 2mgR = 1/2mu²
V² - u² = -4gR
u² = 4gR + V² ---------(1)

and we know, at highest position T = 0 ,
then, V = √gR
Put this in equation (1),
u = √{5gR}

Now, put R = 9m
u = √{5 × 10 × 9} = 15√2m/s

Hence, the speed of object at the lowest position is 15√2m/s

Answer 2

V=√5gr

=√5×10×9

=15√2is our required answer