Question

A stone of mass 100 gram attached to the string of length 50 cm is whirled in a vertical circle by giving velocity at lowest point as 7 metre per second find the velocity at the highest point

Answer 1

this is your Answer I hope you can understand

Answer 2

The velocity at the highest point is 5.422 m/s

Given:

Mass = m = 100 g = 0.1 kg

Radius = r = 50 cm = 0.5 m

Acceleration due to gravity = g = 9.8 $\bold{m/s^2}$

Velocity at the lowest point = $\bold{v_{L}}$ = 7 m/s

To find:

Velocity at the highest point = ?

Formula:

$\bold{v_H=\sqrt{\frac{2(TE_H )}{m}-4gr}}$

Solution:

Total energy at highest point = Kinetic energy at lowest point  

$\bold{TE_H=KE_L}$

Now,

$\bold{\Rightarrow KE=\frac{1}{2} mv_L^2}$

On substituting the given values, we get,

$\bold{KE=\frac{1}{2} \times 0.1 \times (7)^{2}}$

$\bold{\therefore KE=2.45 \ J}$

Now, substituting the values in the velocity at maximum height, we get,

$\bold{v_H=\sqrt{\frac{2(2.45)}{0.1}-(4\times9.8\times0.5)}}$

$\bold{v_H=\sqrt{29.4}}$

$\bold{\therefore v_H=5.422 \ m/s}$