A block of mass m is placed on a smooth wedge of inclination. The whole system is accelerated horizontally so that block does not slip on the wedge Find the i) Acceleration of the wedge Force to be applied on the wedge Force exerted by the wedge on the block .

Explanation

For an observer on the ground
`R sin theta =ma, R cos theta = mg`
`rArr a =g tan theta`
(ii) `F = (M +m) a=(M+m) g tan`●
iii) Force exerted by the wedge on the block
`rArr = (mg)/(cos theta) or R = mg sec theta`
If inclination is given as 1 in x, `sin theta = (1)/(x)`
`tan = (1)/sqrt(x^(2)-1)`
`rArr` Acceleration `a =g tan = (g)/sqrt(x^(2)-1)`

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