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Question

In the given figure, what maximum force F can be applied on wedge of mass M, so that block of mass m does not move with respect to wedge.


A

(M+m)(sinθ+μcosθ)g(cosθμsinθ)
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B

(M+m)(cosθ+μsinθ)g(sinθμcosθ)
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C

(M+m)(sinθμcosθ)g(cosθ+μsinθ)
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D

(M+m)(sinθ+μcosθ)g(sinθ+μcosθ)
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Solution

The correct option is A
(M+m)(sinθ+μcosθ)g(cosθμsinθ)
F = (M + m)a
a = <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> FM+m
Looking m from M



macosθ = <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> fl + mgsinθ
macosθ = μN + mgsinθ
macosθ = μmasinθ + μmgcosθ + mgsinθ
m[cosθ - μsinθ]a = mg[μcosθ + sinθ]
a = (μcosθ+sinθ)g(cosθμsinθ)
F = (M+m)(sinθ+μcosθ)g(cosθμsinθ)

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