Velocity of a particle of mass m as a function of displacement x is given by v = α√ x.

Question

Velocity of a particle of mass m as a function of displacement x is given by v = \(\alpha\sqrt{x}\) .

Work done to move it from x = 0 to x = d is 

(1) \(\frac{m\alpha^2}{2}.d\)

(2) \(m\alpha^2.d\) 

(3) \(\frac{3m\alpha^2d}{2}\) 

(4) \(2m\alpha^2d\)

Answer 1

Correct Option is (1) \(\frac{m\alpha^2}{2}.d\)  

W = \(\Delta{KE}\) 

W = \(\frac{1}{2}m[(\alpha\sqrt{d})^2- (\alpha\sqrt{0})^2]\) 

W = \(\frac{m\alpha^2d}{2}\)