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  • A ball of mass m = 3 Kg is being pulled from the ground on a fixed rough hemispherical surface up to the top of the hemisphere with the help of a light inextensible string. Find work (in Joule) don

A ball of mass m = 3 Kg is being pulled from the ground on a fixed rough hemispherical surface up to the top of the hemisphere with the help of a light inextensible string. Find work (in Joule) done by tension M in the string if the radius of the hemisphere is R = 1 m and the friction coefficient is \mu = 0.6

Assume that the block is pulled with negligible velocity 

Option: 1

-40


Option: 2

48


Option: 3

35


Option: 4

-50


Answers (1)

best_answer

 T = f_r + mg \sin \theta

T = \mu N + mg \sin \theta

N = mg \cos \theta         

   

T = mg \left ( \sin \theta + \mu \cos \theta \right )

W = \int_{0}^{\pi/2} mg (\sin \theta + \mu \cos \theta ) R d \theta\\=mg(-cos\theta+\mu sin\theta)^\frac{\pi}{2}_0 \\ \\ =3 \times 10 \times [ 0.6-(-1) ] = + 48 J

Posted by

Pankaj

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