A body of mass `m =18kg` is placed on an inclined plane the angle of inclination is `alpha =37^(@)` and is attached to the top end of the slope with a thread which is parallel to the slope. Then the plane slope is moved with a horizontal acceleration of a. Friction is negligible.

At what acceleration will the body lose contact with plane .

Options

A. `(40)/(3) m//s^(2)`
B. `7.5 m//s^(2)`
C. `10 m//s^(2)`
D. `5 m//s^(2)`

Answer

A

Explanation

`F.B.D` with respect to plane `F.B.D` with respective to ground
`N + ma sin alpha = mg cos alpha ---(1)`
`T =ma cos alpha + mg sin alpha---(2)`
solving equation (1) and (2) for `N =(3)/(4)mg`
`rArr a = (g)/(12) or a = (5)/(6)m//sec^(2)` and `T =12N`
The body will losse contact for `N =0` For `N=0`
`a =g cot alpha` [From (i)]`a = (40)/(3) m//sec^(2)`
.