A liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid rises at the side. If the radius of the vessel is `5 cm` and the speed of rotation is `4 rev//s`, then the difference in the height of the liquid at the centre of the vessel and its sides is

Options

A. 8 cm
B. 2 cm
C. 40 cm
D. 4 cm

Answer

A

Explanation

`vec(v)=alphahat(i)+betathat(j)`
`(dvec(v))/(dt)=betahat(j)implies a_("total")=beta`
`|vec(v)|=sqrt(alpha^(2)+beta^(2)t^(2))`
`a_(t)=(dv)/(dt)=(2beta^(2)t)/(2sqrt(alpha^(2)+beta^(2)t^(2)))`
`(a_(t))=(beta^(2)((alphasqrt(3))/(beta)))/(sqrt(alpha^(2)+beta^(2)(alpha^(2)3)/(beta^(2))))=(beta^(2)((alphasqrt(3))/(beta)))/(2alpha)`
`a_(t)=(sqrt(3))/(2)beta`
`a_("Normal")=sqrt(a_("total")^(2)-a_(1)^(2))=sqrt(beta^(2)-(3beta^(2))/(4))=(beta)/(2)`