Using law of conservation of energy, "Energy can neither be created nor be destroyed but it can be transformed from one form to another".
That is, sum of Kinetic energy and Potential energy at initial point is equal to the sum of Kinetic energy and Potential energy at final point.
We can say that,
(K.E)1 + (P.E.)1 = (K.E)2 + (P.E)2
1/2 m1 * v1² + m1*g*h1 = 1/2 m2 * v2² + m2* g*h2
For motion in circular path,
Initial velocity v1 is at h1 =0
Final velocity v2 is at h2= d
For rotational motion, inertia is denoted by I.
1/2 I1 * v1² = 1/2 I2* v2² + I2 gd
1/2 I2*v2² = 1/2 I1*v1²- I2 gd
v2²= I1/I2 * v1²- 2 gd
v2= √(I1/12* v1²- 2gd)
The above equation gives the speed of the ball when it reaches the top of circular path in term of I, g and d.
A sun-sized star will spend most of its lifetime as a main sequence star. It is the stage in a star's life cycle where it maintains as a stable nuclear reaction. The sun in our solar system is a clear example of this. The number of years that these stars would spend at this stage depends largely on the mass of the star. These stars would fuse atoms of hydrogen forming them into helium atoms inside their cores. Fusion reactions are continually happening as days and years pass at this stage. Approximately ninety percent of the stars found in the universe are main sequence stars.
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