If a pushing force an angle α with horizontal is applied on a block of mass m placed on horizontal table and angle of function is β, then minimum magnitude of force required to move the block is
A
mgsinβcos[α−β]
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B
mgsinβcos[α+β]
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C
mgsinβsin[α+β]
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D
mgcosβcos[α−β]
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Solution
The correct option is Dmgcosβcos[α−β] μ=tanβ N=mg+Fcosα so, Fsinα=μN Fsinα=μ[mg+Fcosα] F[sinα−μcosα]=μmg F=μmgsinα−μcosα =dtanβ(mg)sinα−tanβcosα =sinβ(mg)sinαcosβ−sinβcosα =sinβ(mg)sin[α−β]