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# Find the Velocity at the Highest Point. - Physics

#### Question

A stone of mass 100 g attached to a string of length 50 cm is whirled in a vertical circle by giving velocity at lowest point as 7 m/s. Find the velocity at the highest point. [Acceleration due to gravity = 9.8 m/s2 ]

#### Solution

Given:-
m = 100 g = 0.1 kg,
r = 50 cm = 0.5m,
g = 9.8 m/s2,
v2 = 7 m/s

To find:- Velocity at the highest point (vH)

Formula:- v_"H"= sqrt((2("TE"_("H")))/"m"-4"gr")

Calculation:-
The total energy at the bottom,
Ebot ( = KE + PE = 1/2 2.45 J )

T.E.(H)= K.E. at lowest point = (1/2)mvL2

∴ T.E(H) = 1/2 x 0.1 x 72

=2.45 J

The total energy at the top,
Etop = KE + PE = 1/2"mv"_1^2 + "mg(2r)"
Etop = 1/2(0.1)v_1^2 + (0.1)(9.8)( 2 xx 0.5 )
Etop = 0.05v_1^2 + 0.98

By the Principle of conservation of energy,
Etop = Ebot
0.05v_1^2 + 0.98 = 2.45

v_1^2 = (2.45 - 0.98 )/(0.05) = 147/5 = 29.4

The required velocity v1 = sqrt(29.4) = 5.422 m/s.

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