Question

the wooden blocks are moving on a smooth horizontal surface such that the mass M remains stationary with respect to the block of mass M as shown in the figure the magnitude of the force P is. ---------------- Please give detailed answer

Answer 1

All surfaces are smooth in the figure. Find F such that block of mass m resting on a wedge of mass M remains stationary with respect to wedge



a) (M−m)gtanθ(M−m)gtan⁡θ b) MgtanθMgtan⁡θ c) MmgtanθMmgtan⁡θ d) (M+m)gtanθ(M+m)gtan⁡θ





The block moves with acceleration a w.r.t ground

a=FM+ma=FM+m

ΣFy=0=>Ncosθ=mgΣFy=0=>Ncos⁡θ=mg

ΣFx=0=>Nsinθ=maΣFx=0=>Nsin⁡θ=ma

a=gtanθa=gtan⁡θ

F=a(M+m)F=a(M+m)

=gtanθ(M+m)=gtan⁡θ(M+m)

Hence d is the correct answer.