A smooth wedge of inclination 37° rises towards the right and is accelerated horizontally towards the right. A block remains at rest relative to the wedge. Take g = 10 m/s², sin37° = 3/5 and cos37° = 4/5. The acceleration of the wedge is:
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Question

A smooth wedge of inclination 37° rises towards the right and is accelerated horizontally towards the right. A block remains at rest relative to the wedge. Take g = 10 m/s², sin37° = 3/5 and cos37° = 4/5. The acceleration of the wedge is:

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G1 Physics · Accepted Answer

In the wedge frame, pseudo force ma acts towards left. Along the incline, pseudo component ma cosθ acts up the plane and gravity component mg sinθ acts down the plane. For relative rest: ma cosθ = mg sinθ. Therefore a = g tanθ = 10×(3/4) = 7.5 m/s².