A trolley containing a liquid slides down a smooth inclined plane of angle `alpha` with the horizontal. Find the angle of inclination `theta` of the free surface with the horizontal.

Options

A. Equal to `alpha`
B. Greater than `alpha`
C. Equal to `(alpha)/(2)`
D. Lesser than `alpha`

Answer

A

Explanation

The effective value of `alpha` at a distance x from the left end is
`alpha=alpha_(1)+((alpha_(2)-alpha_(1))/(l))x`
`Deltal=underset(0)overset(l)intalpha(dx)DeltaT`
`Deltal=underset(0)overset(l)int[alpha_(1)+((alpha_(2)-alpha_(1))/(l))xx]d xx DeltaT`
`Deltal=DeltaT[alpha_(1)l+(alpha_(2)-alpha_(1))/(2l)l^(2)]`
`Deltal=DeltaTl[(alpha_(1)+alpha_(2))/(2)]`