Question

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

Answer 1

The tension at the top is given by,

T=mvt^2/r−mg

or, 

14=1×vt^2/1−1×10=vt^2−10 

(taking g=10)

or, 

vt^2=4

or, 

vt=2

Now loss of potential energy at the bottom is,

Kp=mgh=1×10×2=20

So, total kinetic energy at the bottom is, 

1/2mvb^2=20+1/2mvt^2=20+2=22

So, 

vb=√44=6.6

Answer 2

"According to the given data, Newton’ s law of motion is applied to acquire the tension at the top is given by

$T=\frac { mv_{ t }^{ 2 } }{ r } - mg.$

which is given as T = 14 N,

Thereby,

$14=\frac { mv_{ t }^{ 2 } }{ r } - mg.$

$\Rightarrow 14=\frac { 1\times v_{ t }^{ 2 } }{ 1 } - 1\times 10$

$\Rightarrow v_{ t }^{ 2 }=4$

$\Rightarrow v_{ t }^{ 2 }=2.$

Then the potential energy is lost at the bottom which will help us to derive the equation from conservation of energy. Thereby,

K = mgh

$\Rightarrow K=1\times 10\times 2$

$\Rightarrow K=20$

Therefore, Kinetic energy at the bottom be

$\Rightarrow \frac { 1 }{ 2 } mv_{ b }^{ 2 }=20+\frac { 1 }{ 2 } mv_{ t }^{ 2 }$

$\Rightarrow \frac { 1 }{ 2 } v_{ b }^{ 2 }=20+2=22$

$\Rightarrow v_{ b }^{ 2 }=44$

$\Rightarrow { v }_{ b }=\sqrt { 44 } =6.6$"