Question

The maximum and minimum tensions in the string whirling in a circle of radius 2.5 m with constant velocity are in the ratio 5 : 3. Then its velocity is ____________.

Options

• `sqrt98  "m/s"`

• 7 m/s

• `sqrt 490  "m/s"`

• `sqrt 4.9  "m/s"`

Answer 1

The maximum and minimum tensions in the string whirling in a circle of radius 2.5 m with constant velocity are in the ratio 5 : 3. Then its velocity is `sqrt98  "m/s"`.

Explanation:

Although the particle is travelling in a vertical loop, its speed is believed to be constant in this scenario.

`"Tension at lowest point,"   "T"_"max" = ("mv"^2)/"r" + "mg"`

`"Tension at highest point,"  "T"_"min" = ("mv"^2)/"r" - "mg"`

`therefore "T"_"max"/"T"_"min" = (("mv"^2)/"r" + "mg")/ (("mv"^2)/"r" - "mg")= 5/3`

On solving we get,

v = `sqrt(4gr) = sqrt (4 xx 9.8 xx 2.5) = sqrt 98  "m/s"`