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A trolley containing a liquid slides dow...

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.

A

`theta=alpha/2`

B

`theta=2alpha`

C

`theta=zero`

D

`theta=alpha`

Text Solution

Verified by Experts

The correct Answer is:
D
The acceleration of the trolley is `a=gsintheta` down the inclined plane
`a_(x)=acosalpha=(gsinalpha)cosalpha`
`a_(y)=asinalpha=(gsinalpha)sinalpha=gsin^(2)alpha`
Let `theta` be the angle made by free surface of liquid, then
`tantheta=(a_(x))/(g-a_(y))=(gsinalphacosalpha)/(g-gsin^(2)alpha)=tanalpha`
`theta=alpha`
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