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A block of mass 2 kg slides down the face of a smooth 45° wedge of mass 9 kg as shown in figure. The wedge is placed on a frictionless horizontal surface. Determine the acceleration of the wedge

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1 $m / s^{2}$

2 $m / s^{2}$

none of these

$\frac{10}{3}$ $m / s^{2}$

answer is C.

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Detailed Solution

a is accelerate of block w.r.t. wedge.

For block :
N + mA sin 45° = mg cos 45° ----------- (i)
For wedge: N sin 45° = MA --------------(ii)
From (i) and (ii) A = I0/3 $m / s^{2}$

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