A disc without slipping rolls down a hill with a vertical height of 1000cm. If the disc starts from rest at the top of the hill, what is its magnitude of velocity at the bottom? (11.4 m s⁻¹)


Given:

Vertical height of the hill = h = 1000 cm = 10 m
Value of g = 9.81 m s⁻²

To Find:

The linear speed at bottom of hill= v = ?

Solution:

The formula for linear speed is 

v = `\sqrt frac {4gh}{3}`

Putting values 

v = `\sqrt frac {4 ｘ 9.81 m s⁻² ｘ 10 m}{3}`

v = `\sqrt {130.8 m² s⁻²}`

v = 11.437 m s⁻¹ --------------Ans. 


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