Question

A stone of mass 1 kg is tied with a string and it is whirled in a vertical circle of radius 1m. if tension at highest point is 14n the its velocity at lowest point will be

Answer 1

Hope my attachment will help you

Answer 2

Given that,

Mass = 1 kg

Radius = 1 m

Tension = 14 N

Let v is the velocity at top and v' is at bottom.

We need to calculate the velocity at top

Using balance equation

$T=\dfrac{mv^2}{r}-mg$

Where, m = mass

v = velocity at top

r = radius

T = tension

g = acceleration due to gravity

Put the value into the formula

$14=\dfrac{1\times v^2}{1}-1\times9.8$

$v^2=14-9.8$

$v=\sqrt{14+9.8}$

$v=4.87\ m/s$

We need to calculate the velocity at lowest point

Using conservation of energy

Total kinetic energy at bottom

$\dfrac{1}{2}mv^2=mgh+\dfrac{1}{2}mv^2$

Put the value into the formula

$\dfrac{1}{2}\times1\times v^2=1\times9.8\times2+\dfrac{1}{2}\times1\times(4.87)^2$

$v^2=2\times1\times9.8\times2+\dfrac{1}{2}\times1\times(4.87)^2$

$v^2=51.05845$

$v=\sqrt{51.05845}\ m/s$

$v=7.14\ m/s$

Hence, The velocity at lowest point is 7.14 m/s.