Question

A sphere rolls down an inclined plane through a height h its velocity at the bottom would be

Answer 1

Let mass of each sphere m and radius of sphere is r and h is height of inclined planes .

If V and ω are the linear and angular speed of sphere at bottom of inclined plane .

according to Law of conservation of energy,

Increase in K.E = Decrease in P.E

(1/2)Mv² + (1/2)Iω² = Mgh

For soid sphere, I = (2/5)MR²

angular speed (ω) = v/R

(1/2)Mv² + 1/2× (2/5)MR² × v²/R² = Mgh

(7/10)Mv² = Mgh

v = √{10gh/7}

hence, velocity of sphere at bottom would be √{10gh/7}

Answer 2

$\huge\bold\purple{Answer:-}$

Let mass of each sphere m and radius of sphere is r and h is height of inclined planes .

If V and ω are the linear and angular speed of sphere at bottom of inclined plane .

according to Law of conservation of energy,

Increase in K.E = Decrease in P.E

(1/2)Mv² + (1/2)Iω² = Mgh

For soid sphere, I = (2/5)MR²

angular speed (ω) = v/R

(1/2)Mv² + 1/2× (2/5)MR² × v²/R² = Mgh

(7/10)Mv² = Mgh

v = √{10gh/7}

hence, velocity of sphere at bottom would be √{10gh/7}